scholarly journals On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xinghua Liu ◽  
Hongsheng Xi
Keyword(s):  
Stochastic Stability ◽  
Convex Combination ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Neutral Delay ◽  
Jump Systems

The delay-range-dependent stochastic stability for uncertain neutral Markovian jump systems with interval time-varying delays is studied in this paper. The uncertainties under consideration are assumed to be time varying but norm bounded. To begin with the nominal systems, a novel augmented Lyapunov functional which contains some triple-integral terms is introduced. Then, by employing some integral inequalities and the nature of convex combination, some less conservative stochastic stability conditions are presented in terms of linear matrix inequalities without introducing any free-weighting matrices. Finally, numerical examples are provided to demonstrate the effectiveness and to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

scholarly journals Improved Stability Criteria for Markovian Jump Systems with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yu-cai Ding ◽  
Hui Liu ◽  
Baodan Tian
Keyword(s):  
Convex Combination ◽  
Markovian Jump Systems ◽  
Combination Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Improved Stability ◽  
Lyapunov Matrix ◽  
Delay Dependent ◽  
Jump Systems

The delay-dependent stochastic stability problem of Markovian jump systems with time-varying delays is investigated in this paper. Though the Lyapunov-Krasovskii functional is general and simple, less conservative results are derived by using the convex combination method, improved Wirtinger’s integral inequality, and a slack condition on Lyapunov matrix. The obtained results are formulated in terms of linear matrix inequalities (LMIs). Numerical examples are provided to verify the effectiveness and superiority of the presented results.

scholarly journals Robust Stabilization of Stochastic Markovian Jump Systems with Distributed Delays

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guilei Chen ◽  
Zhenwei Zhang ◽  
Chao Li ◽  
Dianju Qiao ◽  
Bo Sun
Keyword(s):  
Linear Matrix Inequalities ◽  
Robust Stabilization ◽  
Distributed Delays ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Parameter Uncertainties ◽  
Delay Dependent ◽  
Jump Systems

This paper addresses the robust stabilization problem for a class of stochastic Markovian jump systems with distributed delays. The systems under consideration involve Brownian motion, Markov chains, distributed delays, and parameter uncertainties. By an appropriate Lyapunov–Krasovskii functional, the novel delay-dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities. When given linear matrix inequalities are feasible, an explicit expression of the desired state feedback controller is given. The designed controller, based on the obtained criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system. The convenience of the design is greatly enhanced due to the existence of an adjustable parameter in the controller. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed theory.

Finite-time extended dissipative filtering for nonlinear Markovian jump systems with unknown transition rates and time-varying delays

2021 ◽  
pp. 014233122110465
Author(s):  
Yao Wang ◽  
Jun Guo ◽  
Guobao Liu ◽  
Junwei Lu ◽  
Fangyuan Li
Keyword(s):  
Finite Time ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Transition Rates ◽  
Markovian Jump ◽  
Error System ◽  
Jump Systems ◽  
Delay Partitioning ◽  
Nonlinear Markovian Jump Systems

The problem of finite-time filtering for nonlinear Markovian jump systems subject to extended dissipativity with unknown transition rates and time-varying delays is investigated in this paper. Firstly, by constructing novel Lyapunov-Krasovskii functionals and utilizing delay partitioning method, the error system is proved to be stochastically finite-time bounded and extended dissipative. Secondly, in virtue of linear matrix inequalities approach, the desired mode-dependent filter is obtained. Finally, two simulations are illustrated for the purpose of demonstrating the less conservativeness and effectiveness of the proposed method.

scholarly journals Delay-DependentH∞Control for Descriptor Markovian Jump Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Jinghao Li ◽  
Qingling Zhang ◽  
Ding Zhai ◽  
Yi Zhang
Keyword(s):  
Convex Combination ◽  
Markovian Jump Systems ◽  
Delay Systems ◽  
Time Varying ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
Bounded Real Lemma ◽  
Delay Dependent ◽  
Jump Systems ◽  
Varying Delay

This paper is concerned with the delay-dependentH∞control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are regular, impulse-free, and stochastically stable and satisfy a prescribedH∞performance level. Since the reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods.

Mixed filter design for nonlinear singular Markovian jump systems with time-varying delays based on a dissipativity performance index

2018 ◽  
Vol 40 (9) ◽  
pp. 2779-2788 ◽  
Author(s):  
Jing Zuo ◽  
Guobao Liu ◽  
Yunliang Wei ◽  
Zhenda Wei ◽  
Junwen Feng
Keyword(s):  
Filter Design ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Unified Framework ◽  
Decomposition Approach ◽  
Singular Markovian Jump Systems ◽  
Delay Dependent ◽  
Jump Systems

This paper deals with the problem of dissipative filtering for a class of nonlinear singular Markovian Jump systems (SMJSs) with time-varying delays. Our consideration is centered on the design of a mixed filter that can contain both mode-dependent and mode-independent filters in a unified framework. By using a delay-decomposition approach and constructing a mode-dependent stochastic Lyapunov–Krasovskii functional, sufficient delay-dependent conditions are derived in terms of linear matrix inequalities, which guarantee the considered nonlinear SMJSs to be stochastically admissible with a dissipativity performance [Formula: see text]. Based on the conditions, the existence conditions and parameters of the desired filter are obtained. Two numerical examples are given to illustrate the reduced conservatism and the effectiveness of the proposed methods.

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