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.

Stabilization for Stochastic Markovian Jump Systems with Time Delay

2011 ◽  
Vol 403-408 ◽  
pp. 2293-2295
Author(s):  
Yi Zhong Wang
Keyword(s):  
Time Delay ◽  
Robust Stabilization ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
The Mean ◽  
Delay Dependent ◽  
Jump Systems ◽  
Varying Delay

This paper is concerned with the robust stabilization problem for a class of stochastic markovian jump systems with Time-Varying delay. By applying a new Lyapunov-Krasovskii functional, a novel Delay-Dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities(LMIs). When these LMIs are feasible, an explicit expression of the desired state feedback controller is given. Designed controller, based on the obtained criterion, ensures asymptotically stable in the mean square sense of the resulting Closed-Loop system for all admissible uncertainties and time delay.

scholarly journals Delay-dependent stability and stabilization of uncertain discrete-time markovian jump singular systems with time delay

2007 ◽  
Vol 49 (1) ◽  
pp. 111-129 ◽  
Author(s):  
Shuping Ma ◽  
Xinzhi Liu ◽  
Chenghui Zhang
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. With this condition, problems of robust stochastic stability and stabilization are solved, and delay-dependent linear matrix inequalities are obtained. A numerical example is also given to illustrate the effectiveness of this method.2000Mathematics subject classification: primary 39A12; secondary 93C55.

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 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.

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.

Robust Control for Fuzzy Nonlinear Uncertain Systems with Discrete and Distributed Time Delays

2014 ◽  
Vol 69 (10-11) ◽  
pp. 569-580 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Ponnusamy Vadivel ◽  
Kalidass Mathiyalagan ◽  
Ju H. Park
Keyword(s):  
Linear Matrix Inequalities ◽  
Time Delays ◽  
Uncertain Systems ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Distributed Time Delays ◽  
Nonlinear Uncertain Systems

AbstractThis paper addresses the problem of stability and stabilization issue for a class of fuzzy nonlinear uncertain systems with discrete and distributed time delays. By utilizing a new Lyapunov-Krasovskii functional together with free weighting matrix approach, a new set of delay-dependent sufficient conditions are derived which makes the closed loop system robustly asymptotically stable. In particular, the parameter uncertainties are assumed to be norm bounded. Further, a state feedback controller is proposed to guarantee the robust stabilization for uncertain systems and subsequently the controller is constructed in terms of the solution to a set of linear matrix inequalities (LMI). The derived conditions are expressed in the form of linear matrix inequalities which can be efficiently solved via standard LMI toolbox. Further, two numerical examples are provided to demonstrate the effectiveness and less conservatism of the obtained results.

scholarly journals Stabilization of Discrete-Time Markovian Jump Systems via Controllers with Partially Mode-Dependent Characterization

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Chunyan Zhai ◽  
Dingyu Xue ◽  
Shuchen Li ◽  
Guoliang Wang
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Packet Dropout ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stabilizing Controller ◽  
Unreliable Networks ◽  
Jump Systems

A kind of stabilizing controller in terms of being partially mode-dependent is developed for discrete-time Markovian jump systems (MJSs). The property referred to be partially mode-dependent is described by the Bernoulli variable. Based on the established model, the stabilization for MJSs over unreliable networks is considered, where both network-induced delay and packet dropout take place in system modes and states. Such effects of network are taken into account in controller design. All the conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the effectiveness and applicability of the proposed method.

Disturbance-observer-based l2–l∞ control for discrete-time Markovian jump system

2018 ◽  
Vol 40 (9) ◽  
pp. 2807-2812 ◽  
Author(s):  
Linlin Hou ◽  
Haibin Sun
Keyword(s):  
Discrete Time ◽  
Disturbance Observer ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
First Case ◽  
Control Scheme ◽  
Jump Systems

This paper considers the problem of anti-disturbance control for discrete-time Markovian jump systems with multiple disturbances. The controller is constructed via disturbance-observer-based control and l2– l∞ control. The disturbances are divided into two parts. One, in the same channel as the control inputs, is described by an exogenous system. The other is assumed to be bounded with an [Formula: see text] norm. A disturbance observer is presented to estimate and reject the first-case disturbances for discrete-time Markovian jump systems, and an l2– l∞ control scheme is used to attenuate the second-case disturbances. By using linear matrix inequalities, a solvable sufficient condition is developed. Finally, the effectiveness of the proposed control scheme is demonstrated via a numerical example.

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