Event-triggered robust H∞ control for uncertain switched linear systems

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.     

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.     

A geometric approach to H∞ control of nonlinear Markovian jump systems

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.     

An LMI approach to robust reduced-order H ∞ filter design for polytopic uncertain systems

This paper proposes a method for robust reduced-order H _∞ filter design for polytopic uncertain systems, using linear matrix inequalities (LMIs). Sufficient LMI conditions for both robust full- and reduced-order H _∞ filter design are derived. Convex optimization problems are formulated and solved to obtain optimal H _∞ filters by using the resulting LMI conditions. The resulting conditions do not involve any non-convex rank constraints, and thus the proposed method for H _∞ filter design guarantees global optimum solutions. Numerical examples are presented to show the effectiveness of the proposed method. Recommended by Editorial Board member Huanshui Zhang under the direction of Editor Young Il Lee. This work was supported by the Brain Korea 21 Project and the Basic Research Program of the Korea Science and Engineering Foundation under grant R01-2006-000-11373-0. Hyoun-Chul Choi received the B.S., M.S., and Ph.D. degrees in Control and Instrumentation Engineering from Ajou University, Suwon, Korea, in 1995, 1997, and 2006, respectively. He was a Visiting Researcher at Griffith University, Brisbane, Australia, from 2001 to 2002, and a Postdoctoral researcher at Ajou University, Suwon, Korea, from 2006 to 2007. Since 2008, he has been with ASRI, School of Electrical Engineering and Computer Science, Seoul National University, Seoul, Korea, where he is currently a Postdoctoral Researcher. His research interests include LMI-based control, optimal and robust control, network-based control, and mechatronics. Dongkyoung Chwa received the B.S. and M.S. degrees from the Department of Control and Instrumentation Engineering in 1995 and 1997, respectively, and the Ph.D. degree from the School of Electrical and Computer Engineering in 2001, all from Seoul National University, Seoul, Korea. From 2001 to 2003, he was a Postdoctoral Researcher with Seoul National University. In 2003, he was a Visiting Research Fellow at The University of New South Wales, Australian Defence Force Academy, and was the Honorary Visiting Academic at the University of Melbourne, Melbourne, Australia. In 2004, he was a BK21 Assistant Professor with Seoul National University. Since 2005, he has been an Assistant Professor with the Department of Electrical and Computer Engineering, Ajou University, Suwon, Korea. His research interests are nonlinear, robust, and adaptive control theories and their applications to the robotics, underactuated systems including wheeled mobile robots, underactuated ships, cranes, and guidance and control of flight systems. Suk-Kyo Hong received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from Seoul National University, Seoul, Korea, in 1971, 1973, and 1981, respectively. His major graduate research works were centered on speed control of induction motors. He was an Exchange Professor at Rensselaer Polytechnic Institute, Troy, NY, from 1982 to 1983, and at the Institut National de Recherche en Informatique et en Automatique, France, from 1988 to 1989. He has been with the faculty of the Department of Electrical and Computer Engineering, Ajou University, Suwon, Korea, since 1976, and was a Visiting Professor at Griffith University, Australia, in 2001 and 2002. His current research interests include robust robot control, microprocessor applications, factory automation, and computer integrated manufacturing.     

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.     

Robust H ∞ reliable control for a class of uncertain neutral delay systems

This paper deals with the problem of robust reliable control for a class of uncertain neutral delay systems. The aim was to design a state feedback controller such that the plant remained stable for all admissible uncertainties as well as actuator faults among a prespecified subset of actuators or sector-type actuator non-linearity, independently of the delay time. A linear matrix inequality approach was developed to solve the problem addressed with an H X norm bound constraint on disturbance attenuation.     

Robust H∞ containment control for uncertain multi-agent systems with inherent nonlinear dynamics

This article considers the distributed containment control problem of nonlinear multi-agent systems subject to parameter uncertainties and external disturbances. An appropriate controlled output function is defined to quantitatively analyse the effect of external disturbances on the containment control problem. By employing robust H_∞ control approach, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that all followers asymptotically converge to the convex hull spanned by the leaders with the prescribed H_∞ performance under fixed topology. Moreover, the unknown feedback matrix of the proposed protocol is determined by solving only two LMIs with the same dimensions as a single agent. Finally, a numerical example is provided to demonstrate the effectiveness of our theoretical results.     

Design of robust reliable H∞ output feedback control for a class of uncertain linear systems with sensor failure

The problem of robust reliable H_∞ output feedback controller design is investigated for uncertain linear systems with sensor failures within a prespecified subset of sensors. The uncertainty considered here is time-varying norm-bounded parameter uncertainty in the state matrix. The output of a faulty sensor is assumed to be any arbitrary energy-bounded signal. An observer-based output feedback control design is presented which stabilizes the plant and guarantees an H_∞ norm bound on attenuation of augmented disturbances, for all admissible uncertainties as well as sensor failures. The construction of the observer-based output feedback control law requires the positive-definite solutions of two algebraic Riccati equations. The result can be regarded as an extension of existing results on robust H_∞ control and reliable H_∞ control of uncertain linear systems.     

H∞ approach to monotonically convergent ILC for uncertain time-varying delay systems

This paper deals with iterative learning control (ILC) design for uncertain time-delay systems. Monotonic convergence of the resulting ILC process is studied, and a sufficient condition within an H_∞-based framework is developed. It is shown that under this framework, delay-dependent conditions can be obtained in terms of linear matrix inequalities (LMIs), together with formulas for gain matrices design. A numerical example is provided to illustrate the effectiveness of the robust H_∞-based approach to ILC designed via LMIs.     

Decentralized H∞ control for large-scale interconnected nonlinear time-delay systems via LMI approach

In this paper, the problem of H_∞ control of nonlinear large-scale systems with interval time-varying delays in interconnection is considered. The time delays are assumed to be any continuous functions belonging to a given interval involved in both the state and observation output. By constructing a set of new Lyapunov–Krasovskii functionals, which are mainly based on the information of the lower and upper delay bounds, a new delay-dependent sufficient condition for the existence of decentralized H_∞ control is established in terms of linear matrix inequalities (LMIs). The approach is applied to decentralized H_∞ control of uncertain linear systems with interval time-varying delay. Numerical examples are given to show the effectiveness of the obtained results.     

A robust H ∞ control approach for a class of networked control systems with sampling jitter and packet-dropout

This paper is concerned with the robust H _∞ control problem for a class of networked control systems (NCSs) with sampling jitter, short time-varying delays and packet-dropouts. By considering state feedback controller, the close-loop NCS is described as a discrete-time linear switched system model with uncertainties. Based on the linear matrix inequality (LMI) approach, a robust H _∞ condition is proposed to solve the H _∞ stability and stabilization problems for the considered NCS. An illustrative example is provided to demonstrate the effectiveness of the proposed theoretical results.     

Robust H∞ control for uncertain discrete stochastic time-delay systems

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.     

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.     

Robust H ∞ control of uncertain nonlinear switched systems using constructive method

This paper focuses on the problem of robust H _?? control of nonlinear switched systems with parameter uncertainty via the multiple Lyapunov functions (MLFs) approach. The uncertain parameters are assumed to be in a known compact set and are allowed to enter the system nonlinearly. Based on the explicit construction of Lyapunov functions, which avoids solving the Hamilton-Jacobi-Isaacs (HJI) inequalities, sufficient conditions for the solvability of the robust H _?? control problem of cascade nonlinear switched systems are derived under some switching signal. Then, the result is extended to solve the robust H _?? control problem of nonlinear switched systems in strict feedback form. Finally, the effectiveness of the proposed results is illustrated through a simulation example.     

An H∞ suboptimal robust control approach for systems with uncertainties and data dropouts

This paper studies the design of control systems subject to plant uncertainties and data losses in the channel connecting the plant sensor with the controller. The controller design has two main objectives. The first one is to robustify the control law against plant uncertainties. The other one is to achieve good performance by minimising the variance of the error signal. Data losses are modelled as an independent and identically distributed sequence of Bernoulli random variables. For analysis and design, this random variable is replaced by an additive noise plus gain channel model. To cope with structural uncertainties in the model of the plant, an H_∞ control technique is employed. The controller is synthesised in order to make the closed-loop system robust against structural uncertainties of the nominal model, while achieving optimal performance of the system in the presence of dropouts.     

A receding–horizon approach to the nonlinear H∞ control problem

The receding–horizon (RH) methodology is extended to the design of a robust controller of H_∞ type for nonlinear systems. Using the nonlinear analogue of the Fake H_∞ algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input–output map of the closed-loop system obtained with the RH control law has a bounded L₂-gain. Robustness properties of the nonlinear H_∞ control law in face of dynamic input uncertainty are considered.     

Non-fragile robust finite-time H ∞ control for nonlinear stochastic it? systems using neural network

This paper deals with the problem of non-fragile robust finite-time H _?? control for a class of uncertain nonlinear stochastic It? systems via neural network. First, applying multi-layer feedback neural networks, the nonlinearity is approximated by linear differential inclusion (LDI) under statespace representation. Then, a sufficient condition is proposed for the existence of non-fragile state feedback finite-time H _?? controller in terms of matrix inequalities. Furthermore, the problem of nonfragile robust finite-time H _?? control is reduced to the optimization problem involving linear matrix inequalities (LMIs), and the detailed solving algorithm is given for the restricted LMIs. Finally, an example is given to illustrate the effectiveness of the proposed method.     

Robust H-infinity reliable control for a class of nonlinear uncertain neutral delay systems

This paper focuses on the robust H-infinity reliable control for a class of nonlinear neutral delay systems with uncertainties and actuator failures. We design a state feedback controller in terms of linear matrix inequality(LMI) such that the plant satisfies robust H-infinity performance for all adnfissible uncertainties, and actuator failures among a prespecified subset of actuators. An example is also given to illustrate the effectiveness of the proposed approach.