Robust H ∞ networked control for discrete-time fuzzy systems with state quantisation

The problem of robust H _∞ control for uncertain discrete-time Takagi and Sugeno (T-S) fuzzy networked control systems (NCSs) with state quantisation is investigated. A new model of network-based control with simultaneous consideration of network-induced delays and packet dropouts is proposed. By using a fuzzy Lyapunov–Krasovskii functional (LKF), we derive a less conservative delay-dependent stability condition for the closed-loop NCSs. Robust H _∞ fuzzy controller is developed for the asymptotical stabilisation of the NCSs. Since it is not expressed as strict LMI conditions, the cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. A numerical example shows the feasibility applications of the proposed technique.     

Dynamic output feedback H ∞ control for affine fuzzy systems

This article investigates the problem of designing H _∞ dynamic output feedback controllers for nonlinear systems, which are described by affine fuzzy models. The system outputs have been chosen as premise variables, which can guarantee that the plant and the controller always switch to the same region. By using a piecewise Lyapunov function and adding slack matrix variables, a piecewise-affine dynamic output feedback controller design method is obtained in the formulation of linear matrix inequalities (LMIs), which can be efficiently solved numerically. In contrast to the existing work, the proposed approach needs less LMI constraints and leads to less conservatism. Finally, numerical examples illustrate the effectiveness of the new result.     

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H_∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H_∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.     

Robust H 2 and H ∞ control of discrete-time systems with polytopic uncertainties via dynamic output feedback

This paper addresses the problem of robust H ₂ and H _∞ control of discrete linear time-invariant (LTI) systems with polytopic uncertainties via dynamic output feedback. The problem has been known to be difficult when a parameter dependent Lyapunov function is to be applied for a less conservative design due to non-convexity. Our approach is based on a novel bounding technique that converts the non-convex optimization into a convex one together with a line search, which is simple but may be conservative. To further reduce the design conservatism, an algorithm based on the sequentially linear programming method (SLPMM) is proposed. A numerical example is given which demonstrates the feasibility of the proposed design methods.     

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

H∞ output feedback control for fuzzy systems with immeasurable premise variables: Discrete-time case

This paper discusses H_∞ output feedback control of discrete-time Takagi–Sugeno fuzzy systems with immeasurable premise variables. When we consider the output feedback control of Takagi–Sugeno fuzzy systems, the selection of premise variables plays an important role. If the premise variable is the state of the system, then a fuzzy system describes a wide class of nonlinear systems. However, the state is not measurable in the output feedback control problem. In this case, a control design of the underlying nonlinear system based on parallel distributed compensation is infeasible because a controller depends on the immeasurable state variable. In this paper, we introduce a new method to treat fuzzy systems with immeasurable premise variables and consider a design method of H_∞ output feedback control problem. We formulate this fuzzy control problem as a robust H_∞ control of an uncertain system. Numerical examples are given to illustrate our methods.     

The output feedback control for uncertain nonholonomic systems

This paper considers the problems of almost asymptotic stabilization and global asymptotic regulation （GAR） by output feedback for a class of uncertain nonholonomic systems. By combining the nonsmooth change of coordinates and output feedback domination design together, we construct a simple linear time-varying output feedback controller, which can universally stabilize a whole family of uncertain nonholonomic systems. The simulation demonstrates the effectiveness of the proposed controller.     

H ∞ output feedback stabilisation of linear discrete-time systems with impulses

This article addresses the issue of designing an H _∞ output feedback controller for linear discrete-time systems with impulses. First, a new concept of H _∞ output feedback stabilisation for general linear discrete-time systems with impulses is introduced. Then sufficient linear matrix inequality conditions for the stabilisation and H _∞ performance of general discrete systems with impulses are proposed. In addition, the result is applied to resolve typical output feedback control problems for systems with impulses, such as the decentralised H _∞ output feedback control and the simultaneous H _∞ output feedback control. Finally, a numerical simulation is also presented to illustrate the effectiveness of the proposed 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.     

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.     

Robust H∞ sliding mode control for uncertain discrete singular T-S fuzzy Markov jump systems

This paper mainly explored the problem of stability in terms of discrete singular T-S fuzzy Markov jump systems with uncertainties and external disturbances. A new sliding mode controller is proposed for this type of system. Firstly, a common sliding surface that can be shared by all subsystems of discrete singular systems is designed, so the jumping effects could be weakened. Secondly, the proof of stochastic admissibility of the closed-loop dynamic system is provided by deriving the linear matrix inequality (LMI) technique. Thirdly, an appropriate sliding mode control (SMC) law is designed to satisfy the discrete reaching condition. And, finally, a simulation is offered to illustrate the effectiveness of the derived results.     

Robust mixed H 2/H ∞ filtering for discrete-time delay fuzzy systems

A robust mixed H ₂/H∞ filtering problem for discrete-time fuzzy systems subject to parameter uncertainties and multiple time-varying delays in state variables is addressed in this paper. The uncertain systems are expressed as Takagi-Sugeno fuzzy models with linear nominal parts and norm-bounded uncertainties. The main objective is to design a stable filter which minimizes a guaranteed cost index and achieves a prescribed H∞ performance under worst-case disturbance. Based on Lyapunov theory, sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of LMIs. Therefore, stable filters are obtained with existing convex algorithms. Lastly, two examples are given to illustrate the proposed design methodology.     

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.     

Non-fragile robust H ∞ control for uncertain spacecraft rendezvous system with pole and input constraints

This article investigates the robust H _∞ control problem for a class of spacecraft rendezvous systems with parameter uncertainties and subject to input constraint, pole constraint and external and controller perturbations. Based on the Lyapunov theory, a sufficient condition for the existence of the non-fragile robust state-feedback controller is given in terms of linear matrix inequalities (LMIs). Then, proper non-fragile controller design can be cast as a convex optimisation problem subject to LMI constraints. With the obtained controller, the spacecraft rendezvous mission can be accomplished. An illustrative example is provided to show the effectiveness of the proposed control design method.     

Robust H ∞ control for T–S fuzzy systems with time-varying delay

This article focuses on the problem of robust H _∞ control for uncertain T–S fuzzy systems with time-varying delay. By employing a novel technique, new delay-dependent stabilisation conditions for the existence of a robust H _∞ controller are obtained based on the parallel distributed compensation method. The result obtained is an important contribution as it establishes a new way that can reduce the conservatism without imposing any restrictions and computational efforts at the same time. In this article, all the conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using LMI optimisation techniques. Two numerical examples are given to demonstrate the merits of the approach proposed in this article. Finally, application to control a truck-trailer is also given to demonstrate the effectiveness of the proposed design method.     

Robust H ∞ control for a class of uncertain mechanical systems

In this article, the problem of H _∞ control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass, damping and stiffness matrices. Two approaches, norm-bounded and linear fractional transformation (LFT) uncertainty formulations, are considered. By using a new Lyapunov–Krasovskii functional approach, combined with the advanced techniques for achieving delay dependence, improved robust H _∞ state-feedback controller design methods are developed. The existence condition for admissible controllers is formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimisation problem subject to LMI constraints. If the optimisation problem is solvable, a desired controller can be readily constructed. The result for the norm-bounded uncertainty case improves the existing ones in terms of design conservatism, and that for the LFT uncertainty case represents the first attempt in this direction. An illustrative example is provided to show the effectiveness and advantage of the proposed controller design methodologies.     

Robust control for a class of uncertain switched fuzzy systems

A model of uncertain switched fuzzy systems whose subsystems are uncertain fuzzy systems is presented. Robust controllers for a class of switched fuzzy systems are designed by using the Lyapunov function method. Stability conditions for global asymptotic stability are developed and a switching strategy is proposed. An example shows the effectiveness of the method.