Quadratic stabilizability and H∞ control of linear discrete‐time stochastic uncertain systems

This paper considers quadratic stabilizability and H_∞ feedback control for stochastic discrete‐time uncertain systems with state‐ and control‐dependent noise. Specifically, the uncertain parameters considered are norm‐bounded and external disturbance is an l²‐square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H_∞ state and output feedback H_∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_∞ controllable. Sufficient conditions for the existence of the desired robust H_∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.     

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.     

Robust H∞ Filtering For Uncertain Stochastic Time‐Delay Systems

This paper deals with the problem of robust H_∞ filtering for uncertain stochastic systems. The system under consideration is subject to time‐varying norm‐bounded parameter uncertainties and unknown time delays in both the state and measurement equations. The problem we address is the design of a stable filter that ensures the robust stochastic stability and a prescribed H_∞ performance level for the filtering error system irrespective of all admissible uncertainties and time delays. A suffient condition for the solvability of this problem is proposed and a linear matrix inequality approach is developed for the design of the robust H_∞ filters. An illustrative example is provided to demonstrate the effctiveness of the proposed approach.     

Robust H∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems

This paper studies the H_∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems. Firstly, by using the linear matrix inequality (LMI) method, a sufficient condition is obtained for the robustly stochastic stability. Secondly, the robust H_∞ state feedback controller is designed, such that the considered system is not only internally stochastically stabilizable but also satisfies the robust H_∞ performance. The desired robust H_∞ controller is obtained via solving some LMIs. Finally, one example is provided to demonstrate the effectiveness of the proposed method.     

STOCHASTIC STABILIZATION AND H∞ CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS

In this paper, robust stochastic stabilization and H_∞ control for a class of uncertain discrete‐time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state‐feedback controller design procedure for discrete time‐delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H_∞ control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results.     

Robust stabilization and H∞ control of uncertain stochastic time‐delay systems with nonlinear perturbation

This paper investigates the problem of delay‐dependent robust stochastic stabilization and H_∞ control for uncertain stochastic nonlinear systems with time‐varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H_∞ control for uncertain stochastic system with time‐varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed‐loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust finite‐time H∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

In this article, the problem of robust finite‐time H_∞ synchronization control is investigated for a class of uncertain discrete‐time master‐slave systems with Markovian switching parameters in the observer‐based case. Parameter uncertainties are assumed to be norm‐bounded, and the polyhedral character is utilized to describe the transition probabilities of nonhomogeneous Markov chain. By using stochastic Lyapunov function method and finite‐time analysis techniques, novel sufficient conditions that include the master‐slave parameters are obtained for designing an observer‐based finite‐time H_∞ synchronization control law in terms of linear matrix inequalities. The effectiveness of the proposed theoretical scheme is finally demonstrated by some simulations.     

Delay‐dependent robust H∞ controller synthesis for discrete singular delay systems

In this paper, the problems of delay‐dependent robust stability analysis, robust stabilization and robust H_∞ control are investigated for uncertain discrete‐time singular systems with state delay. First, by making use of the delay partitioning technique, a new delay‐dependent criterion is given to ensure the nominal system to be regular, causal and stable. This new criterion is further extended to singular systems with both delay and parameter uncertainties. Then, without the assumption that the considered systems being regular and causal, robust controllers are designed for discrete‐time singular time‐delay systems such that the closed‐loop systems have the characteristics of regularity, causality and asymptotic stability. Moreover, the problem of robust H_∞ control is solved following a similar line. The obtained results are dependent not only on the delay, but also on the partitioning size and the conservatism is non‐increasing with reducing partitioning size. These results are shown, via extensive numerical examples, to be much less conservative than the existing results in the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

H∞ control for conic non-linear jump systems with partially unknown transition probabilities

In this paper, the robust H_∞ control problem is investigated for conic non-linear stochastic jump systems with partially unknown transition probabilities and uncertain exogenous disturbance. By resorting to free-connection weighting matrix approach and matrix decomposition technique, two less conservative criteria are derived such that the nominal or uncertain Markovian jump non-linear systems are stochastically stable and have an H_∞ attention level. In addition, stochastic H_∞ control analysis and design are tackled for the class of stochastic jump systems by applying fixed weighting matrix method. Two numerical examples are presented to verify the effectiveness of theoretical results.     

Robust stability and H∞ control for uncertain discrete Markovian jump singular systems with mode‐dependent time‐delay

The robust stochastic stability, stabilization and H_∞ control for mode‐dependent time‐delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a standard linear system, and delay‐dependent linear matrix inequalities (LMIs) conditions for the mode‐dependent time‐delay discrete Markovian jump singular systems to be regular, causal and stochastically stable, and stochastically stable with γ‐disturbance attenuation are obtained, respectively. With these conditions, robust stabilization problem and robust H_∞ control problem are solved, and the LMIs sufficient conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper. Copyright © 2008 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.     

ROBUST H∞ CONTROL FOR UNCERTAIN STOCHASTIC SYSTEMS WITH MARKOVIAN SWITCHING AND TIME‐VARYING DELAYS

This paper is concerned with the problem of robust H_∞ control for uncertain stochastic systems with Markovian jump parameters and time‐varying state delays. A linear matrix inequality approach is developed and state feedback controllers are designed, which guarantee mean square asymptotic stability of the closed‐loop system and a prescribed H_∞ performance level for all modes and admissible uncertainties. A numerical example is provided to demonstrate the application of the proposed method.     

Robust H∞ control for uncertain singular systems with state delay

This paper addresses the problem of robust H_∞ control for uncertain continuous singular systems with state delay. The singular system under consideration involves state time delay and time‐invariant norm‐bounded uncertainty. Based on the linear matrix inequality (LMI) approach, we design a memoryless state feedback controller law, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is not only regular, impulse free and stable, but also meets an H_∞‐norm bound constraint on disturbance attenuation. A numerical example is provided to demonstrate the applicability of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Robust Fault Detection for Discrete‐Time Nonlinear Impulsive Switched Systems

This paper deals with the problem of robust fault detection for discrete‐time nonlinear impulsive switched systems. The fault detection filter is used as the residual generator, in which the filter parameters are dependant on the system mode. Attention is focused on designing the robust fault detection filter. The problem of robust fault detection is converted into an H_∞‐filtering problem. A sufficient condition for the solvability of this problem is established by a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

H∞ Control of Linear Discrete‐Time Systems With Norm‐Bounded Nonlinear Uncertainties

In this paper, robust H_∞ control of a class of discrete‐time uncertain systems in state‐space form with linear nominal parts and norm‐bounded nonlinear uncertainties in both state and output equations is discussed. Such systems have a unique characterisic; that is, the two norm‐bounded nonlinear uncertainties have the equivalent representation by means of time‐varying and norm‐bounded linear uncertainties. To overcome the conservativenss of [5], the two nonlinear uncertainty sets are considered to be different. Then, by converting such systems into related discrete‐time linear systems with time‐varying and norm‐bounded linear uncertainties, we obtain that a sufficient condition for robust H_∞ control of such systems is equivalent to the solvability of the same problem of the related linear uncertain systems, which is solvable by means of a linear algebraic Riccati inequality.     

LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME‐DELAY SYSTEMS WITH NONLINEAR DISTURBANCES

This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete‐time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full‐order and reduced‐order filters guaranteeing a prescribed noise attenuation level in an H∞ or l₂‐l∞ sense with respect to all energy‐bounded noise disturbances for all admissible uncertainties and time delays. Both delay‐dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays.     

Robust mixed H2/H∞ delayed state feedback control of uncertain neutral systems with time‐varying delays

This paper considers the problem of robust mixed H₂/H_∞ delayed state feedback control for a class of uncertain neutral systems with time‐varying discrete and distributed delays. Based on the Lyapunov–Krasovskii functional theory, new required sufficient conditions are established in terms of delay‐range‐dependent linear matrix inequalities for the stability and stabilization of the considered system using some free matrices. The desired robust mixed H₂/H_∞ delayed state feedback control is derived based on a convex optimization method such that the resulting closed‐loop system is asymptotically stable and satisfies H₂ performance with a guaranteed cost and a prescribed level of H_∞ performance, simultaneously. Finally, a numerical example is given to illustrate the effectiveness of our approach. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust non‐minimal order filter and smoother design for discrete‐time uncertain systems

This paper is concerned with the design of robust non‐minimal order H_∞ filters for uncertain discrete‐time linear systems. The uncertainty is assumed to be time‐invariant and to belong to a polytope. The novelty is that a convex filtering design procedure with Linear Matrix Inequality constraints is proposed to synthesize guaranteed‐cost filters with order greater than the order of the system. An H_∞‐norm bound for the transfer‐function from the system input to the filtering error is adopted as performance criterion. The non‐minimal order filters proposed generalize other existing filters with augmented structures from the literature and can provide better performance. An extension to the problem of robust smoothing is proposed as well. The procedure is illustrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust L2−L∞ Filtering for Stochastic Systems with Discrete and Distributed Time‐Varying Delays

This paper is devoted to the problem of robust L₂–L_∞ filtering for a class of stochastic systems with both discrete and distributed time‐varying delays. The objective is to design a full‐order filter such that the resulting filtering error system is stochastically asymptotically stable with a prescribed L₂–L_∞ performance satisfied. Delay‐dependent sufficient condition for the existence of the filter is obtained in terms of linear matrix inequalities (LMIs). And the filter design method is proposed, while the explicit expression for the desired filter is also given. Numerical examples are included to illustrate the benefit and the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A new approach to network‐based H∞ control for stochastic systems

This paper deals with the problem of network‐based H_∞ control for a class of uncertain stochastic systems with both network‐induced delays and packet dropouts. The networked control system under consideration is represented by a stochastic model, which consists of two successive delay components in the state. The uncertainties are assumed to be time varying and norm bounded. Sufficient conditions for the existence of H_∞ controller are proposed to ensure exponentially stable in mean square of the closed‐loop system that also satisfies a prescribed performance. The conditions are expressed in the frame of linear matrix inequalities (LMIs), which can be verified easily by means of standard software. Two practical examples are provided to show the effectiveness of the proposed techniques. Copyright © 2011 John Wiley & Sons, Ltd.