scholarly journals On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-23
Author(s):  
Xinghua Liu ◽  
Hongsheng Xi
Keyword(s):  
Exponential Stability ◽  
Lyapunov Stability Theory ◽  
Markovian Jump Systems ◽  
Time Varying ◽  
Transition Rates ◽  
Stability Criteria ◽  
Markovian Jump ◽  
Rate Dependent ◽  
Partially Known Transition Rates ◽  
Jump Systems

The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciprocally convex lemma, and free-weighting matrices. The corresponding results are extended to the uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals Stability Analysis for Neutral Delay Markovian Jump Systems with Nonlinear Perturbations and Partially Unknown Transition Rates

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Xinghua Liu ◽  
Hongsheng Xi
Keyword(s):  
Exponential Stability ◽  
Lyapunov Theory ◽  
Markovian Jump Systems ◽  
Time Varying ◽  
Transition Rates ◽  
Nonlinear Perturbations ◽  
Markovian Jump ◽  
Neutral Delay ◽  
Rate Dependent ◽  
Jump Systems

The problem of exponential stability for the uncertain neutral Markovian jump systems with interval time-varying delays and nonlinear perturbations is investigated in this paper. This study starts from the corresponding nominal systems with known and partially unknown transition rates, respectively. By constructing a novel augmented Lyapunov functional which contains triple-integral terms and fully utilizes the bound of the delay, the delay-range-dependent and rate-dependent exponential stability criteria are developed by the Lyapunov theory, reciprocally convex lemma, and free weighting matrices. Then, the results about nominal systems are extended to the uncertain case. Finally, numerical examples are given to demonstrate the effectiveness of the proposed methods.

Positive L1-gain filter design for positive Markovian jump systems with time-varying delay and incomplete transition rates

2016 ◽  
Vol 94 (9) ◽  
pp. 877-883
Author(s):  
Wenhai Qi ◽  
Xianwen Gao ◽  
Yonggui Kao
Keyword(s):  
Filter Design ◽  
Markovian Jump Systems ◽  
Time Varying ◽  
Transition Rates ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
Positive Markovian Jump Systems ◽  
Error System ◽  
Jump Systems ◽  
Varying Delay

This paper deals with the problem of positive L1-gain filter design for positive Markovian jump systems with time-varying delay and incomplete transition rates. By implying an appropriate co-positive type Lyapunov function and free-connection weighting vectors, sufficient conditions for stochastic stability of the filtering error system are established. Then, the L1-gain performance is analyzed. Based on the obtained results, a positive full-order filter is designed to ensure that the corresponding filtering error system is positive and stochastically stable with L1-gain performance. All the conditions are derived in linear programming. Finally, the obtained theoretical results are demonstrated by a numerical example.

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.

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