Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Resilient decentralized stabilization of interconnected time‐delay systems with polytopic uncertainties

Decentralized delay‐dependent local stability and resilient feedback stabilization methods are developed for a class of linear interconnected continuous‐time systems. The subsystems are time‐delay plants which are subjected to convex‐bounded parametric uncertainties and additive feedback gain perturbations while allowing time‐varying delays to occur within the local subsystems and across the interconnections. The delay‐dependent local stability conditions are established at the subsystem level through the construction of appropriate Lyapunov–Krasovskii functional. We characterize decentralized linear matrix inequalities (LMIs)‐based delay‐dependent stability conditions by deploying an injection procedure such that every local subsystem is delay‐dependent robustly asymptotically stable with an γ‐level ??₂‐gain. Resilient decentralized state‐feedback stabilization schemes are designed, which takes into account additive gain perturbations such that the family of closed‐loop feedback subsystems enjoys the delay‐dependent asymptotic stability with a prescribed γ‐level ??₂‐gain for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on representative examples. Copyright © 2010 John Wiley & Sons, Ltd.     

STABILIZATION AND H∞ CONTROL FOR UNCERTAIN STOCHASTIC TIME‐DELAY SYSTEMS VIA NON‐FRAGILE CONTROLLERS

This paper considers the problems of robust non‐fragile stochastic stabilization and H_∞ control for uncertain time‐delay stochastic systems with time‐varying norm‐bounded parameter uncertainties in both the state and input matrices. Attention is focused on the design of memoryless state feedback controllers which are subject to norm‐bounded uncertainties. For both the cases of additive and multiplicative controller uncertainties, delay‐independent sufficient conditions for the solvability of the above problems are obtained. The desired state feedback controller can be constructed by solving a certain linear matrix inequality.     

Global quadratic stabilization of a class of nonlinear systems

The problem of quadratic stabilization for a class of nonlinear systems is examined in this paper. By employing a well-known Riccati approach, we develop a technique for designing a state feedback control law which quadratically stabilizes the system for all admissible uncertainties. This state feedback control law consists of linear and nonlinear feedback control terms. The linear feedback control term is generalized from a well-known H_∞ result, while the nonlinear term can be viewed as a correcting term for the presence of nonlinear bounded uncertainty. This stabilization result is extended to static output feedback and to systems for which the nonlinear uncertainty satisfies generalized matching conditions. Furthermore, we point out that in the presence of nonlinear uncertainty the global quadratic stability may be destroyed by some arbitrary small mismatched uncertainty in the matrix, and proceed to establish the region of semi-global quadratic stability of the controlled system. © 1998 John Wiley & Sons, Ltd.     

H ∞ control of networked control systems with state quantisation

This article addresses the problem of controller design for networked control systems over digital communication. The systems under consideration are stabilised via state feedback, where the effects of sampled signal, state quantisation, network-induced delay and packet dropout are considered. The proposed delay-dependent stability criteria are formulated in the form of a linear matrix inequality, which ensure asymptotic stability and a prescribed H _∞ performance level for networked control systems with admissible uncertainties. Maximum allowable delay bound of networked control systems is obtained by solving a convex optimisation problem. Furthermore, a numerical example is given to illustrate the effectiveness of the main result.     

Robust finite-time <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of stochastic jump systems

This paper provides the stochastic finite-time stabilization and H _∞ control problem of Markov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The finite-time H _∞ controller via state feedback is provided to guarantee the stochastic finite-time bounded-ness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible uncertainties and unknown time-delays. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. Simulation results illustrate the effectiveness of the developed approaches.     

Simultaneous robust normalization and delay‐dependent robust H∞ stabilization for singular time‐delay systems with uncertainties in the derivative matrices

This paper investigates the problem of simultaneous robust normalization and delay‐dependent H_∞ control for a class of singular time‐delay systems with uncertainties. Not only the state and input matrices but also the derivative matrices of the considered systems are assumed to have uncertainties. New sufficient conditions for the existence of a proportional plus derivative state feedback H_∞ controller are derived as LMIs such that the closed‐loop singular system is normal, stable, and guarantee a specific level of performance. Specially, a static state feedback H_∞ controller alone or a state‐derivative feedback H_∞ controller alone can unite to be dealt with by applying our proposed method. Two simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper. Copyright © 2014 John Wiley & Sons, Ltd.