Dynamic file grouping for load balancing in streaming media clustered server systems

A dynamic file grouping strategy is presented to address the load balancing problem in streaming media clustered server systems. This strategy increases the server cluster availability by balancing the workloads among the servers within a cluster. Additionally, it improves the access hit ratio of cached files in delivery servers to alleviate the limitation of I/O bandwidth of storage node. First, the load balancing problem is formulated as a two layers semi-Markov switching state-space control process. This analytic model captures the behaviors of streaming media clustered server systems accurately, and is with constructional flexibility and scalability. Then, a policy iteration based reinforcement learning algorithm is proposed to optimize the file grouping policy online. By utilizing the features of the event-driven policy, the proposed optimization algorithm is adaptive and with less computational cost. Simulation results demonstrate the effectiveness of the proposed approach. Recommended by Editor Hyun Seok Yang. This work was supported by the National Natural Science Foundation of China under grant Nos. 60774038, 60574065, National 863 HI-TECH Research & Development Plan of China under grant Nos. 2006AA01Z114, 2008AA01A317, Natural Science Foundation of Anhui Province under grant No. 070412063, Graduate Student Innovation Foundation of USTC under grant No. KD2006036, and Science Research Development Foundation of HFUT under grant No. GDBJ2008-045. Qi Jiang received the B.S. degree in Industrial Electrical Automation from Southeast University in 1989 and the Ph.D. degree in Control Science and Engineering from University of Science and Technology of China in 2008. He is currently a Post-doc in USTC. His research interests include optimization and control of stochastic dynamic systems, and performance analysis and optimization of network communication systems. Hong-Sheng Xi received the M.S. degree in Applied Mathematics from University of Science and Technology of China in 1977. He is currently a Professor in Department of Automation, USTC. His research interests include discrete event dynamic systems, performance analysis and optimization of network communication systems, robust control, and network security. Bao-Qun Yin received the B.S. degree in Mathematics from Sichuan University in 1985, the M.S. degree in Applied Mathematics and the Ph.D. degree in Pattern Recognition and Intelligent Systems from University of Science and Technology of China in 1993 and 1998, respectively. He is currently a Professor in Department of Automation, USTC. His research interests include discrete event dynamic systems, and Markov decision processes.     

Relaxed stability condition and state feedback H ∞ controller design for T-S fuzzy systems

In this paper, a fuzzy Lyapunov approach is presented for stability analysis and state feedback H _∞ controller design for T-S fuzzy systems. A new stability condition is obtained by relaxing the ones derived in previous papers. Then, a set of LMI-based sufficient conditions which can guarantee the existence of state feedback H _∞ controller for T-S fuzzy systems is proposed. In comparison with the existing literature, the proposed approach not only provides more relaxed stability conditions but also ensures better H _∞ performance. The effectiveness of the proposed approach is shown through two numerical examples. Recommended by Editor Young-Hoon Joo. Xiao-Heng Chang received the B.E. and M.S. degrees from Liaoning Technical University, China, in 1998 and 2004, respectively, and the Ph.D. degree from Northeastern University, China, in 2007. He is currently a Lecturer in the School of Information Science and Engineering, Bohai University, China. His research interests include fuzzy control and robust control as well as their applications. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, nonfragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society.     

LMI stability criterion with less variables for time-delay systems

Slack variables approach is an important technique for tackling the delay-dependent stability problem for systems with time-varying delay. In this paper, a new delay-dependent stability criterion is presented without introducing any slack variable. The technique is based on a simply integral inequality. The result is shown to be equivalent to some existing ones but includes the least number of variables. Thus, redundant selection and computation can be avoided so that the computational burden can be largely reduced. Numerical examples are given to illustrate the effectiveness of the proposed stability conditions. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. The authors would like to thank the Associate Editor and the Reviewers for their very helpful comments and suggestions. This work was supported in part by the Funds for Creative Research Groups of China under Grant 60821063, by the State Key Program of National Natural Science of China under Grant 60534010, by the Funds of National Science of China under Grant 60674021, 60774013, 60774047, National 973 Program of China under Grant No. 2009CB320604, and by the Funds of Ph.D. program of MOE, China under Grant 20060145019 and the 111 Project B08015. Xun-Lin Zhu received the B.S. degree in Applied Mathematics from Information Engineering Institute, Zhengzhou, China, in 1986, the M.S. degree in basic mathematics from Zhengzhou University, Zhengzhou, China, in 1989, and the Ph.D. degree in Control Theory and Engineer-ing from Northeastern University, Shenyang, China, in 2008. Currently, he is an Associate Professor at Zhengzhou University of Light Industry, Zhengzhou, China. His research interests include neural networks and networked control systems. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, non-fragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society. Tao Li was born in 1979. He is now pursuing a Ph.D. degree in Research Institute of Automation Southeast University, China. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Chong Lin received the B.Sci and M.Sci in Applied Mathematics from the Northeastern University, China, in 1989 and 1992, respectively, and the Ph.D in Electrical and Electronic Engineering from the Nanyang Technological University, Singapore, in 1999. He was a Research Associate with the University of Hong Kong in 1999. From 2000 to 2006, he was a Research Fellow with the National University of Singapore. He is currently a Profesor with the Institute of Complexity Science, Qingdao University, China. His current research interests are mainly in the area of systems analysis and control. Lei Guo was born in 1966. He received the Ph.D. degree in Control Engineering from Southeast University (SEU), PR China, in 1997. From 1999 to 2004, he has worked at Hong Kong University, IRCCyN (France), Glasgow University, Loughborough University and UMIST, UK. Now he is a Professor in School of Instrument Science and Opto-Electronics Engineering, Beihang University. He also holds a Visiting Professor position in the University of Manchester, UK and an invitation fellowship in Okayama University, Japan. His research interests include robust control, stochastic systems, fault detection, filter design, and nonlinear control with their applications.     

A new approach to fuzzy modeling and control for nonlinear dynamic systems: Neuro-fuzzy dynamic characteristic modeling and adaptive control mechanism

The study on nonlinear control system has received great interest from the international research field of automatic engineering. There are currently some alternative and complementary methods used to predict the behavior of nonlinear systems and design nonlinear control systems. Among them, characteristic modeling (CM) and fuzzy dynamic modeling are two effective methods. However, there are also some deficiencies in dealing with complex nonlinear system. In order to overcome the deficiencies, a novel intelligent modeling method is proposed by combining fuzzy dynamic modeling and characteristic modeling methods. Meanwhile, the proposed method also introduces the low-level learning power of neural network into the fuzzy logic system to implement parameters identification. This novel method is called neuro-fuzzy dynamic characteristic modeling (NFDCM). The neuro-fuzzy dynamic characteristic model based overall fuzzy control law is also discussed. Meanwhile the local adaptive controller is designed through the golden section adaptive control law and feedforward control law. In addition, the stability condition for the proposed closed-loop control system is briefly analyzed. The proposed approach has been shown to be effective via an example. Recommended by Editor Young-Hoon Joo. This work was jointly supported by National Natural Science Foundation of China under Grant 60604010, 90716021, and 90405017 and Foundation of National Laboratory of Space Intelligent Control of China under Grant SIC07010202. Xiong Luo received the Ph.D. degree from Central South University, Changsha, China, in 2004. From 2005 to 2006, he was a Postdoctoral Fellow in the Department of Computer Science and Technology at Tsinghua University. He currently works as an Associate Professor in the Department of Computer Science and Technology, University of Science and Technology Beijing. His research interests include intelligent control for spacecraft, intelligent optimization algorithms, and intelligent robot system. Zengqi Sun received the bachelor degree from Tsinghua University, Beijing, China, in 1966, and the Ph.D. degree from Chalmers University of the Technology, Gothenburg, Sweden, in 1981. He currently works as a Professor in the Department of Computer Science and Technology, Tsinghua University. His research interests include intelligent control of robotics, fuzzy neural networks, and intelligent flight control. Fuchun Sun received the Ph.D. degree from Tsinghua University, Beijing, China, in 1998. From 1998 to 2000, he was a Postdoctoral Fellow in the Department of Automation at Tsinghua University, where he is currently a Professor in the Department of Computer Science and Technology. His research interests include neural-fuzzy systems, variable structure control, networked control systems, and robotics.     

Neuro-fuzzy generalized predictive control of boiler steam temperature

Power plants are nonlinear and uncertain complex systems. Reliable control of superheated steam temperature is necessary to ensure high efficiency and high load-following capability in the operation of modem power plant. A nonlinear generalized predictive controller based on neuro-fuzzy network （NFGPC） is proposed in this paper. The proposed nonlinear controller is applied to control the superheated steam temperature of a 200MW power plant. From the experiments on the plant and the simulation of the plant, much better performance than the traditional controller is obtained,     

Adaptive filtering under minimum information divergence criterion

Traditional filtering theory is always based on optimization of the expected value of a suitably chosen function of error, such as the minimum mean-square error (MMSE) criterion, the minimum error entropy (MEE) criterion, and so on. None of those criteria could capture all the probabilistic information about the error distribution. In this work, we propose a novel approach to shape the probability density function (PDF) of the errors in adaptive filtering. As the PDF contains all the probabilistic information, the proposed approach can be used to obtain the desired variance or entropy, and is expected to be useful in the complex signal processing and learning systems. In our method, the information divergence between the actual errors and the desired errors is chosen as the cost function, which is estimated by kernel approach. Some important properties of the estimated divergence are presented. Also, for the finite impulse response (FIR) filter, a stochastic gradient algorithm is derived. Finally, simulation examples illustrate the effectiveness of this algorithm in adaptive system training. Recommended by Editorial Board member Naira Hovakimyan under the direction of Editor Jae Weon Choi. This work was supported in part by the National Natural Science Foundation of China under grants 50577037 and 60604010. Badong Chen received the B.S. and M.S. degrees in Control Theory and Engineering from Chongqing University, Chongqing, China, in 1997 and 2003, respectively, and the Ph.D. degree in Computer Science and Technology from Tsinghua University, Beijing China, in 2008. He is currently a Postdoctor of the Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, China. His research interests are in signal processing, adaptive control, and information theoretic aspects of control systems. Yu Zhu received the B.S. of Radio Electronics in 1983 at Beijing Normal University, and the M.S. of Computer Applications in 1993, and the Ph.D. of Mechanical Design and Theory in 2001 at China University of Mining & Technology. He is now a Professor of the Institute of Manufacturing Engineering of Department of Precision and Mechanology of Tsinghua University. His current research interests are parallel machanism and theory, two photon micro-fabrication, ultra-precision motion system and motion control. Jinchun Hu received the Ph.D. in Control Science and Engineering from Nanjing University of Science and Technology, Nanjing, China, in 1998. Since then, he has been a postdoctoral researcher in Nanjing University of Aeronautics and Astronautics in 1999 and Tsinghua University in 2002 respectively. His research interests are in flight control, aerial Robot and intelligent control. Dr. Hu is currently an Associate Professor of the Department of Computer Science and Technology of Tsinghua University, Beijing, China. Zengqi Sun received the B.S. degree from the Department of Automatic Control, Tsinghua University, Beijing, China, in 1966 and the Ph.D. degree in Control Engineering from the Chalmas University of Technology, Sweden, in 1981. He is currently a Professor of the Department of Computer Science and Technology, Tsinghua University, Beijing, China. He is the author or coauthor of more than 100 paper and eight books on control and robotics. His research interests include robotics, intelligent control, fuzzy system, neural networks, and evolutionary computation.     

A selective attention-based contextual perception approach for a humanoid robot

A humanoid robot is always flooded by sensed information when sensing the environment, and it usually needs significant time to compute and process the sensed information. In this paper, a selective attention-based contextual perception approach was proposed for humanoid robots to sense the environment with high efficiency. First, the connotation of attention window (AW) is extended to make a more general and abstract definition of AW, and its four kinds of operations and state transformations are also discussed. Second, the attention control policies are described, which integrate intensionguided perceptual objects selection and distractor inhibition, and can deal with emergent issues. Distractor inhibition is used to filter unrelated information. Last, attention policies are viewed as the robot’s perceptual modes, which can control and adjust the perception efficiency. The experimental results show that the presented approach can promote the perceptual efficiency significantly, and the perceptual cost can be effectively controlled through adopting different attention policies.     

Robust fault detection filter design for uncertain LTI systems based on new bounded real lemma

This paper concerns the problem of robust fault detection filter design for uncertain linear time-invariant (LTI) systems with both model uncertainty and disturbances. Firstly, the fault detection filter design is formulated to H _∞ model-matching problem. Secondly, based on a new bounded real lemma, a sufficient condition for the existence of the robust fault detection filter is constructed in term of linear matrix inequalities (LMIs). Owing on the introduction of the tuning parameter and slack variables in obtained LMI condition, the proposed design method can provide higher fault detection sensitivity performance than the existing one. Finally, an illustrative example is employed to demonstrate the effectiveness of the proposed approach. Recommended by Editorial Board member Bin Jiang under the direction of Editor Jae Weon Choi. This work was supported by Postdoctoral Fundation of Jiangsu Province under grant 0901026c and Key Laboratory of Education Ministry for Image Processing and Intelligent Control under grant 200805. Tao Li received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is a postdoctoral researcher with the same university. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Lingyao Wu received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is an Assistant Professor in the Research Institute of Automation Southeast University. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Xinjiang Wei was born in Dongying, China, in 1977. He received the B.S. degrees from Yantai Normal University, China in 1999, M.S. degrees from Bohai University in 2002, and the Ph.D. degree in Department of Information from Northeastern University in 2005. From 2006 to Present, he was with Ludong University as an Associate Professor. From 2006 to 2009, he was a Postdoctoral Fellow at Southeast University. His research interests include robust control, nonlinear control, and fuzzy control.     

Semi-supervised discriminative classification with application to tumorous tissues segmentation of MR brain images

Due to the large data size of 3D MR brain images and the blurry boundary of the pathological tissues, tumor segmentation work is difficult. This paper introduces a discriminative classification algorithm for semi-automated segmentation of brain tumorous tissues. The classifier uses interactive hints to obtain models to classify normal and tumor tissues. A non-parametric Bayesian Gaussian random field in the semi-supervised mode is implemented. Our approach uses both labeled data and a subset of unlabeled data sampling from 2D/3D images for training the model. Fast algorithm is also developed. Experiments show that our approach produces satisfactory segmentation results comparing to the manually labeled results by experts.

Delay-dependent robust stability criteria for delay neural networks with linear fractional uncertainties

This article investigates the problem of robust stability for neural networks with time-varying delays and parameter uncertainties of linear fractional form. By introducing a new Lyapunov-Krasovskii functional and a tighter inequality, delay-dependent stability criteria are established in term of linear matrix inequalities (LMIs). It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach. Recommended by Editorial Board member Naira Hovakimyan under the direction of Editor Young-Hoon Joo. This work was supported by the National Science foundation of China under Grant no. 60774013 and Key Laboratory of Education Ministry for Image Processing and Intelligent Control under grant no. 200805. Tao Li received the Ph.D. degree in The Research Institute of Automation Southeast University, China. Now He is an Assistant Professor in Department of Information and Communication, Nanjing University of Information Science and Technology. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Lei Guo received the Ph.D. degree in the Research Institute of Automation Southeast University, China. From 1999 to 2004, he has worked at Hong Kong University, IRCCyN (France), Glasgow University, Loughborough University and UMIST, UK. Now He is a Professor in School of Instrument Science and Opto-Electronics Engineering, Beihang University. His current research interests include robust control, fault detection and diagnosis. Lingyao Wu received the Ph.D. degree in The Research Institute of Automation Southeast University, China. Now He is an Assistant Professor in the Research Institute of Automation Southeast University. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Changyin Sun received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is a Professor in the Research Institute of Automation Southeast University. His current research interests include timedelay systems, neural networks.     

Nonlinear inversion-based output tracking control of a boiler-turbine unit

The capability to perform fast load-following has been an important issue in the power industry. An output tracking control system of a boiler-turbine unit is developed. The system is composed of stable inversion and feedback controller. The stable inversion is implemented as a feedforward controller to improve the load-following capability, and the feedback controller is utilized to guarantee the stability and robustness of the whole system. Loop-shaping H∞ method is used to design the feedback controller and the final controller is reduced to a multivariable PI form. The output tracking control system takes account of the multivariable, nonlinear and coupling behavior of boiler-turbine system, and the simulation tests show that the control system works well and can be widely applied.     

Robust control design of a class of nonlinear systems in polynomial lower-triangular form

This paper investigates the problem of global robust stabilization for a wide class of nonlinear systems, called polynomial lower-triangular form (pLTF), which expands LTF to a more general case. The aim is explicitly constructing the smooth controller for the class of systems with static uncertainties, by adding and modifying a power integrator in a recursive manner. The pLTF relaxes the restrictions on the structure of the normal LTF and enlarges the family of systems that are stabilizable. Examples are also provided to show the practical usage of this class of systems and the effectiveness of the design method. Recommended by Editorial Board member Hyungbo Shim under the direction of Editor Jae Weon Choi. Bing Wang received the B.S. degree from the Huazhong University of Science and Technology, and the Ph.D. degree from the University of Science and Technology of China, in 1998 and 2006, respectively. He is currently working in College of Electrical Engineering, Hohai University. His research interests include robust control, nonlinear control and power systems. Haibo Ji received the B.S. and Ph.D. degrees in Mechanical Engineering from ZheJiang University and Beijing University in 1984 and 1990 respectively. He is currently a Professor in the Dept. of Automation, USTC. His research interests include nonlinear control and adaptive control. Jin Zhu received the B.S. and Ph.D. degrees in Control Science and Engineering from University of Science & Technology of Chinain 2001 and 2006 respectively. He is currently a Post-doc in Han-Yang University, Korea. His research interests include Markovian jump systems and nonlinear control.     

Survey on the stability of networked control systems

The insertion of the communication network in the feedback control loop makes the analysis and design of a network control system more complex, and induces some issues that degrade the control system’s performance and even cause system instability. The main aspects are focused on the stability analysis of Network Control Systems (NCSs) with network-induced delays, data packet dropouts, and multiple-packet transmission. These issues must be considered in the design of an NCS. This work summarizes the main research results, and remarks on some related handling approaches and techniques. The main purpose of the survey is to present the new research state of NCSs and to point out some fields of future work.     

Mixed frequency small gain state feedback control with application to insulin pumps

This paper considers the state feedback control synthesis problem for linear continuous-time systems with small gain specifications in mixed frequency ranges. A new method for designing the state feedback controllers is developed in the framework of linear matrix inequality (LMI) approach. Finally, the effectiveness of the proposed method in comparison with the available result is illustrated via an application to insulin pumps. Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Jae Weon Choi. This work was supported in part by the Funds for Creative Research Groups of China (No. 60821063), the State Key Program of National Natural Science of China (Grant No. 60534010), National 973 Program of China (Grant No. 2009CB320604), the Funds of National Science of China (Grant No. 60674021), the 111 Project (B08015) and the Funds of PhD program of MOE, China (Grant No. 20060145019). Xiao-Ni Zhang received the B.E. and M.S. degree from the Shenyang Normal University, China, in 1999 and 2003, respectively, and a Ph.D. candidate at Northeastern University. Her research interest covers robust control, mixed frequency optimal control and reliable control. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, nonfragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society.     

Delay-dependent robust H ∞ control for uncertain fuzzy Markovian jump systems

This paper is concerned with the problem of delay-dependent robust H _∞ control for uncertain fuzzy Markovian jump systems with time delays. The purpose is to design a mode-dependent state-feedback fuzzy controller such that the closed-loop system is robustly stochastically stable and satisfies an H _∞ performance level. By introducing slack matrix variables, a delay-dependent sufficient condition for the solvability of the problem is proposed in terms of linear matrix inequalities. An illustrative example is finally given to show the applicability and effectiveness of the proposed method. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. This work is supported by the National Science Foundation for Distinguished Young Scholars of P. R. China under Grant 60625303, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20060288021, and the Natural Science Foundation of Jiangsu Province under Grant BK2008047. Yashun Zhang received the B.S. and M.S. degrees in Control Science and Control Engineering from Hefei University of Science and Technology in 2003 and 2006. He is currently a Ph.D. student in Control Science and Control Engineering, Nanjing University of Science and Technology. His research interests include fuzzy control, sliding mode control and nonlinear control. Shengyuan Xu received the Ph.D. degree in Control Science and Control Engineering from Nanjing University of Science and Technology in 1999. His research interests include robust filtering and control, singular systems, time-delay systems and nonlinear systems. Jihui Zhang is a Professor in the School of Automation Engineering of Qingdao University, China. His main areas of interest are discrete event dynamic systems, production planning and control, and operations research.     

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.     

A further note on overshoot estimation in pole placements

Recently, it is proved in the literature that for a given controllable pair （A, B） with A ∈R^n×n, B ∈R^n×m, and any λ ≥ 1, a gain matrix K can be designed so that ‖e^（A＋BK）t‖ ≤Mλ^Le^-λt, where M and L are constants independent of λ. Here, we show that M and L can be chosen much smaller than that proposed above. As a consequence, the estimation on overshoot of a transition matrix can be bounded more precisely. This can be regarded as a complement to the existing result.     

A General Probability Formula of the Number of Location Areas＇ Boundaries Crossed by a Mobile Between Two Successive Call Arrivals

Mobility management is a challenging topic in mobile computing environment. Studying the situation of mobiles crossing the boundaries of location areas is significant for evaluating the costs and performances of various location management strategies. Hitherto, several formulae were derived to describe the probability of the number of location areas‘ boundaries crossed by a mobile. Some of them were widely used in analyzing the costs and performances of mobility management strategies. Utilizing the density evolution method of vector Markov processes, we propose a general probability formula of the number of location areas‘ boundaries crossed by a mobile between two successive calls. Fortunately, several widely-used formulae are special cases of the proposed formula.