H∞ filtering for singular Markovian jump systems with time delay

The problem of H_∞ filtering is considered for singular Markovian jump systems with time delay. In terms of linear matrix inequality (LMI) approach, a delay‐dependent bounded real lemma (BRL) is proposed for the considered system to be stochastically admissible while achieving the prescribed H_∞ performance condition. Based on the BRL and under partial knowledge of the jump rates of the Markov process, both delay‐dependent and delay‐independent sufficient conditions that guarantee the existence of the desired filter are presented. The explicit expression of the desired filter gains is also characterized by solving a set of strict LMIs. Some numerical examples are given to demonstrate the effectiveness of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ deconvolution filtering for uncertain singular Markovian jump systems with time‐varying delays

The problem of H_∞ deconvolution filter design for a class of singular Markovian jump systems with time‐varying delays and parameter uncertainties is considered in this paper. By constructing a more comprehensive stochastic Lyapunov‐Krasovskii functional, novel delay‐dependent conditions are established to guarantee the filtering error system is not only stochastically admissible, but also satisfies a prescribed H_∞‐norm level for all admissible uncertainties. The desired filter parameters can be obtained by solving a set of strict linear matrix inequalities. Two examples and an electrical RLC circuit example are employed to verify the effectiveness and usefulness of the proposed methods in the paper. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust H∞ filtering for a class of Markovian jump systems with time‐varying delays based on delta operator approach

In this paper, the robust H_∞ filtering problem for a class of discrete Markovian jump systems with time‐varying delays and linear fractional uncertainties is investigated based on delta operator approach. Based on Lyapunov‐Krasovskii functional in delta domain, new delay‐dependent sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired jump H_∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into the delta operator systems framework. Numerical examples are given to illustrate the effectiveness of the developed techniques. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exponential H∞ filter design for stochastic time‐varying delay systems with Markovian jumping parameters

In this paper, the exponential H_∞ filter design problem is investigated for a general class of stochastic time‐varying delay system with Markovian jumping parameters. The stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time‐varying. Attention is focused on the design of mean‐square exponentially stable and Markovian jump filter such that the filtering error systems are mean‐square exponentially stable and the estimation error satisfies a given H_∞ performance. By introducing some slack matrix variables, delay‐dependent sufficient conditions for the solvability of the above problem are presented in terms of linear matrix inequalities (LMIs). In addition, the decay rate can be a given positive value without any other constraints. When the proposed LMIs are feasible, an explicit expression of the desired H_∞ filter can be given. A numerical example is provided to illustrate the effectiveness of the proposed design approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Stability and stabilization of discrete‐time singular Markov jump systems with time‐varying delay

The stochastic stability and stochastic stabilization of time‐varying delay discrete‐time singular Markov jump systems are discussed. For full and partial knowledge of transition probabilities cases, delay‐dependent linear matrix inequalities (LMIs) conditions for the systems to be regular, causal and stochastically stable are given. Sufficient conditions are proposed for the existence of state feedback controller in terms of LMIs. Finally, two numerical examples to illustrate the effectiveness of the method are given. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

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.     

Delay‐dependent robust control for singular discrete‐time Markovian jump systems with time‐varying delay

The problem of delay‐dependent robust stabilization for uncertain singular discrete‐time systems with Markovian jumping parameters and time‐varying delay is investigated. In terms of free‐weighting‐matrix approach and linear matrix inequalities, a delay‐dependent condition is presented to ensure a singular discrete‐time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state‐feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

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 Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

H∞ control for discrete‐time Markovian jump systems with partial information on transition probabilities

This paper focuses on mode‐dependent H_∞ state‐feedback control for a class of discrete‐time Markovian jump systems (MJSs) with partial information on transition probabilities (TPs). The augmented free‐connection weighting matrices are introduced by considering the influence of partial information of TPs on discrete‐time MJSs and the disturbance input on the state vector. As a result, the less conservative stability criterion and bounded real lemma (BRL) of MJSs with partly unknown TPs are obtained. Then the sufficient conditions for designing the mode‐dependent H_∞ controllers are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness and the merits of the proposed method.     

Delay‐dependent robust H2/H∞ control for time‐delay systems with polytopic uncertainty

In this paper, new separated delay‐dependent H_∞ and H₂ performance criteria are derived for a class of time‐delay systems. Then they are extended to design a multiobjective robust H₂/H_∞ controller for polytopic uncertain systems with time delay. All the conditions are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

This paper aims to solve the H_∞ stabilization problem for networked semi‐Markovian jump systems subject to randomly occurring uncertainties by an improved event‐triggered technique. A new measurement error that is defined as the difference value between the latest transmitted data and the mean value of both current data and latest transmitted data is introduced into the event‐triggered condition. Compared with traditional dynamic event‐triggered scheme, more unexpected data could be avoided to be transmitted, which is demonstrated in the simulation through sufficient comparison experiments. Furthermore, by employing a Lyapunov‐Krasovskii functional method and a free‐weighting matrix method, sufficient conditions are derived to guarantee the stabilization of the closed‐loop semi‐Markovian jump time‐delay system with uncertainties and a prescribed performance index. Then, a codesign method for H_∞ controller gains and event‐triggered parameters is presented. Finally, simulations are given to verify the effectiveness of our improved dynamic event‐triggered scheme.     

Finite‐Time H∞ Filtering for Nonlinear Continuous‐Time Singular Semi‐Markov Jump Systems

The stochastic finite‐time H_∞ filtering issue for a class of nonlinear continuous‐time singular semi‐Markov jump systems is discussed in this paper. Firstly, sufficient conditions on singular stochastic H_∞ finite‐time boundedness for the filtering error system are established. The existence of a unique solution for the corresponding system is also ensured. Secondly, based on the bounds of the time‐varying transition rate, without imposing constraints on slack variables, a novel approach to finite‐time H_∞ filter design is proposed in the forms of strict LMIs, which guarantees the filtering error system is singular stochastic H_∞ finite‐time bounded and of a unique solution. Compared with the existing ones, the presented results reveal less conservativeness. Finally, one numerical example is exploited to testify the advantage of the proposed design technique.     

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.     

Delay‐dependent stability criterion and H∞ analysis for Markovian jump systems with time‐varying delays

This paper deals with the problems of stochastic stability and H_∞ analysis for Markovian jump linear systems with time‐varying delays. In terms of linear matrix inequalities, a less conservative delay‐dependent stability criterion for Markovian jump systems is proposed by constructing a different Lyapunov‐Krasovskii functional and introducing improved integral‐equalities approach, and a sufficient condition is derived from the H_∞ performance. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐range‐dependent H∞ control for Markovian jump systems with mode‐dependent time delays

This paper considers mean‐square exponential stability and H_∞ control problems for Markovian jump systems (MJSs) with time delays which are time‐varying in an interval and depend on system mode. By exploiting a novel Lyapunov‐Krasovskii functional which takes into account the range of delay, and by making use of some techniques, new delay‐range‐dependent stability result and bounded real lemma for MJSs are obtained, where the introduction of the lower bound of delay is shown to be advantageous for reducing conservatism. Moreover, a sufficient condition for the solvability of the H_∞ control problem is derived in terms of linear matrix inequalities. Finally, illustrative examples are presented to show the advantage and effectiveness of the proposed approaches. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Event‐triggered filter design for Markovian jump delay systems with nonlinear perturbation using quantized measurement

This paper deals with the problem of mixed passivity and H_∞ filter design for a class of Markovian jump delay systems with nonlinear perturbation under event‐triggered scheme and quantization. Firstly, based on an integral inequality, a new sufficient condition for the stochastic stability and performance analysis of the filtering error system is proposed. Secondly, a mode‐dependent condition for the solvability of the filter design problem is given in terms of linear matrix inequalities (LMIs). The filter parameters can be derived using feasible solutions of the presented LMIs. Finally, three numerical examples are given to illustrate the effectiveness and advantages of the proposed filter design method.     

Delay‐range‐dependent robust H∞ filtering for uncertain systems with interval time‐varying delays

This paper is concerned with the problem of delay‐range‐dependent robust H_∞ filtering for systems with time‐varying delays in a range. The aim of this problem is to design a filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable with a prescribed H_∞ level. The desired filter can be constructed by solving a set of linear matrix inequalities (LMIs). An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society