Exponential stability for positive Markovian jump systems with switching transition rates subject to average dwell time approach

2017 ◽  
Author(s):  
Wenhai Qi ◽  
Guangdeng Zong
Keyword(s):  
Exponential Stability ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Markovian Jump Systems ◽  
Transition Rates ◽  
Markovian Jump ◽  
Positive Markovian Jump Systems ◽  
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.

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.

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