Finite-time dissipativity analysis and design for stochastic Markovian jump systems with generally uncertain transition rates and time-varying delay

2015 ◽  
Vol 39 (6) ◽  
pp. 807-819 ◽  
Author(s):  
Xianwen Gao ◽  
Lian Lian ◽  
Wenhai Qi
Keyword(s):  
Finite Time ◽  
Time Varying ◽  
Transition Rates ◽  
Markovian Jump ◽  
Analysis And Design ◽  
Time Varying Delay ◽  
Generally Uncertain Transition Rates ◽  
Jump Systems ◽  
Dissipativity Analysis ◽  
Varying Delay

The paper is concerned with finite-time dissipativity analysis and design for stochastic Markovian jump systems with generally uncertain transition rates and time-varying delay. By constructing a more appropriate Lyapunov–Krasovskii functional, sufficient conditions for finite-time dissipativity of the underlying system are first proposed. Then, a state feedback controller is designed such that the closed-loop Markovian jump system is finite-time dissipative. These sufficient criteria are derived in the form of linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the validity of the main results.

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 observer-based control for Markovian jump systems with time-varying generally uncertain transition rates

2020 ◽  
pp. 014233122096470
Author(s):  
Mengjun Li ◽  
Xiaohang Li ◽  
Dunke Lu
Keyword(s):  
Finite Time ◽  
External Disturbance ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Transition Rates ◽  
Markovian Jump ◽  
Generally Uncertain Transition Rates ◽  
Jump Systems

This paper addresses the finite-time observer-based control for Markovian jump systems with time-varying generally uncertain transition rates. In order to estimate the states, a suitable observer is designed, in which both external disturbance and Brownian motion exist. In order to solve the complex time-varying transition rates, a quantization mechanism is raised to prove the closed-loop system and the observer error system be stable. Sufficient conditions of the existences of both the observer and the observer-based controller are derived in terms of linear matrix inequalities. Eventually, two practical examples are given to testify the correctness of the results.

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