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1.
Yashun Zhang Shengyuan Xu Jihui Zhang 《International Journal of Control, Automation and Systems》2009,7(4):520-529
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. 相似文献
2.
In this paper, robust H∞ control for a class of uncertain stochastic Markovian jump systems (SMJSs) with interval and distributed time-varying delays is investigated. The jumping parameters are modelled as a continuous-time, finite-state Markov chain. By employing the Lyapunov-Krasovskii functional and stochastic analysis theory, some novel sufficient conditions in terms of linear matrix inequalities are derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method comparing with some existing results. 相似文献
3.
In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones. 相似文献
4.
Bo Song Jianwei Xia Yun Zou Qingwei Chen 《International journal of systems science》2013,44(4):633-642
This article investigates the problem of robust H ∞ filtering for a class of nonlinear neutral stochastic time-delay systems with norm-bounded parameter uncertainties. The nonlinearities are assumed to satisfy the global Lipschitz conditions. By solving a set of certain linear matrix inequalities, an H ∞ filter is designed, which ensures both the robust stochastic stability and a prescribed H ∞ performance of the filtering error system for all admissible uncertainties. A numerical example is given to show the effectiveness of the design method proposed in this article. 相似文献
5.
Feng-Hsiag Hsiao 《International journal of systems science》2013,44(4):351-360
A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and Rk of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach. 相似文献
6.
Xudong Zhao Qingshuang Zeng 《International Journal of Control, Automation and Systems》2010,8(2):482-489
This paper deals with the H ∞ performance analysis problems for a class of Markovian jump systems with partially known transition rates and time-delays which are time varying and depend on system mode. Following the recent study on the class of systems, improved sufficient conditions for H ∞ performance of the underlying systems are derived in form of LMI by constructing a new Lyapunov-Krasovskii functional. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach. 相似文献
7.
Weimin Chen Qian Ma Lanning Wang Huiling Xu 《International journal of systems science》2018,49(1):58-67
This paper investigates the exponential stabilisation and H∞ control problem of neutral stochastic delay Markovian jump systems. First, a delay feedback controller is designed to stabilise the neutral stochastic delay Markovian jump system in the drift part. Second, sufficient conditions for the existence of feedback controller are proposed to ensure that the resulting closed-loop system is exponentially stable in mean square and satisfies a prescribed H∞ performance level. Finally, numerical examples are provided to show the effectiveness of the proposed design methods. 相似文献
8.
Ya-Kun Su Bing Chen Qi Zhou Chong Lin 《International journal of systems science》2013,44(8):1568-1579
This article deals with the problem of H ∞ filter design for nonlinear discrete-time systems with norm-bounded parameter uncertainties and time-varying delays. A new Lyapunov function and free-weighting matrix method are used for filtering design, consequently, a delay-dependent design method is first proposed in terms of linear matrix inequalities, which produces a less conservative result. Finally, numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method. 相似文献
9.
10.
This paper investigates the problem of reliable finite-time H∞ control for one class of uncertainsingular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. Continuous fault model is more general and practical to serve as the actuator fault. Time delay is a kind of positive time-varying differentiable bounded delays. First, based on a state estimator the resulting closed-loop error system is constructed and sufficient criteria are provided to guarantee that the augmented system is singular stochastic finite-time boundedness and singular stochastic H∞ finite-time boundedness in both normal and fault cases via constructing a delay-dependent Lyapunov–Krasonskii function. Then, the gain matrices of state-feedback controller and state estimator are fixed by solving a feasibility problem in terms of linear matrix inequalities through decoupling technique, respectively. Finally, numerical examples are given to show the validity of the proposed design approach. 相似文献
11.
12.
This paper concerns the problem of H∞ filtering for piecewise homogeneous Markovian jump nonlinear systems. Different from the existing studies in the literatures, the existence of variations in transition rates for Markovian jump nonlinear systems is considered. The purpose of the paper is to design mode-dependent and mode-independent filters, such that the dynamics of the filtering errors are stochastic integral input-to-state stable with H∞ performance index. Using the linear matrix inequality method and the Lyapunov functional method, sufficient conditions for the solution to the H∞ filtering problem are derived. Finally, three examples are proposed to illustrate the effectiveness of the given theoretical results. 相似文献
13.
14.
This paper focuses on the optimal robust reliable H∞ control for a class of uncertain nonlinear systems with actuator faults. A new method of annihilating uncertain matrix is proposed. Based on this approach, a new method of disposing of the phenomenon of uncertain matrices multiplication is provided. In accordance with the method, the optimal robust reliable H∞ control problem for uncertain nonlinear systems is settled by employing state feedback, in terms of linear matrix inequality (LMI). Finally, two illustrative examples are given to show the feasibility and validity of the proposed method. 相似文献
15.
16.
Zhongwei Lin Jizhen Liu Weihai Zhang Yuguang Niu 《International journal of control》2013,86(9):1833-1845
This paper first discusses the H∞ control problem for a class of general nonlinear Markovian jump systems from the viewpoint of geometric control theory. Following with the updating of the Markovian jump mode, the appropriate diffeomorphism can be adopted to transform the system into special structures, which establishes the basis for the geometric control of nonlinear Markovian jump systems. Through discussing the strongly minimum-phase property or the strongly γ-dissipativity of the zero-output dynamics, the H∞ control can be designed directly without solving the traditional coupled Hamilton–Jacobi inequalities. A numerical example is presented to illustrate the effectiveness of our results. 相似文献
17.
Yuanqing Xia Li Li Magdi S. Mahmoud Hongjiu Yang 《International journal of systems science》2013,44(2):272-284
The problem of H ∞ filtering for nonlinear singular Markovian jumping systems with interval time-varying delays is investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Furthermore, the derivative of the time-varying delay function can be larger than one. With partial knowledge of the jump rates of the Markov process, a new delay-range-dependent bounded real lemma for the solvability of the jump system is obtained based on the Lyapunov–Krasovskii functional, which is in terms of strict linear matrix inequalities (LMIs). When these LMIs are feasible, an expression of a desired H ∞ filter is given. Numerical examples are given to illustrate the effectiveness of the developed techniques. 相似文献
18.
This article mainly addresses the H ∞ stabilisation problem for a class of networked control systems (NCSs) with random input delays in the continuous-time domain. A Markov jump linear system (MJLS) model with two jump parameters is developed which takes both the sensor-to-controller and controller-to-actuator delays into account. Based on such a MJLS, a new Lyapunov–Krasovskii functional is proposed to establish a delay-dependent H ∞ stabilisation criterion in terms of linear matrix inequalities (LMIs), and a mode-dependent state-feedback controller of NCSs can be determined. Two numerical examples are included to illustrate the derived result. 相似文献
19.
Yiwen Qi Pengyu Zeng Wen Bao Zhigang Feng 《International journal of systems science》2017,48(15):3172-3185
In this paper, an event-triggering scheme is implemented in uncertain switched linear systems with time-varying delays and exogenous disturbance. Instead of standard periodically time-triggered, sampled-data control systems, the event-triggered control systems sample data only when an event, typically defined as some performance error exceeding a tolerant bound, occurs. Specifically, considering the disturbance existing in the system, the event-triggered robust H∞ control problem is studied. In order to guarantee the robust H∞ performance, the event-triggered full state feedback control, multiple Lyapunov functions method and state-dependent switching law are utilised to construct sufficient conditions in terms of linear matrix inequalities. In particular, since the event-triggered signals and switching signals may interlace with each other, the influence from them on the analysis of robust H∞ performance is clarified. Subsequently, sufficient design conditions of the sub-controllers’ gains are further presented. Moreover, the Zeno problem is discussed to exclude continuously triggering and sampling. Finally, numerical simulations are provided to verify the feasibility of the proposed approach. 相似文献
20.
《Systems & Control Letters》2004,51(3-4):203-215
This paper deals with the problems of robust stabilization and robust H∞ control for discrete stochastic systems with time-varying delays and time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed-loop system for all admissible uncertainties, while for the robust H∞ control problem, a state feedback controller is designed such that, in addition to the requirement of the robust stochastic stability, a prescribed H∞ performance level is also required to be satisfied. A linear matrix inequality (LMI) approach is developed to solve these problems, and delay-dependent conditions for the solvability are obtained. It is shown that the desired state feedback controller can be constructed by solving certain LMIs. An example is provided to demonstrate the effectiveness of the proposed approach. 相似文献