Exponential stability and L1-gain analysis for positive time-delay Markovian jump systems with switching transition rates subject to average dwell time

2018 ◽  
Vol 424 ◽  
pp. 224-234 ◽  
Author(s):  
Wenhai Qi ◽  
Ju H. Park ◽  
Jun Cheng ◽  
Yonggui Kao ◽  
Xianwen Gao
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Markovian Jump Systems ◽  
Transition Rates ◽  
Markovian Jump ◽  
Positive Time ◽  
Jump Systems

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.

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