Quantitative exponential stability and stabilisation of discrete-time Markov jump systems with multiplicative noises

2017 ◽  
Vol 11 (16) ◽  
pp. 2886-2892 ◽  
Author(s):  
Zhiguo Yan ◽  
Weihai Zhang ◽  
Ju H. Park ◽  
Xiaoping Liu
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Multiplicative Noises ◽  
Jump Systems

scholarly journals Stability Analysis for a Class of Discrete-Time Nonhomogeneous Markov Jump Systems with Multiplicative Noises

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Shaowei Zhou ◽  
Xiaoping Liu ◽  
Bing Chen ◽  
Hongxia Liu
Keyword(s):  
Discrete Time ◽  
Transition Probability ◽  
Convex Polytope ◽  
Linear Matrix ◽  
Infinite Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Multiplicative Noises ◽  
Jump Systems

This paper is concerned with a class of discrete-time nonhomogeneous Markov jump systems with multiplicative noises and time-varying transition probability matrices which are valued on a convex polytope. The stochastic stability and finite-time stability are considered. Some stability criteria including infinite matrix inequalities are obtained by parameter-dependent Lyapunov function. Furthermore, infinite matrix inequalities are converted into finite linear matrix inequalities (LMIs) via a set of slack matrices. Finally, two numerical examples are given to demonstrate the validity of the proposed theoretical methods.

scholarly journals Dissipativity-based asynchronous control for discrete-time singular Markov jump systems with multiplicative noises

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141985161
Author(s):  
Xiao Lu ◽  
Jiaqiang Yan ◽  
Haixia Wang ◽  
Chunyang Sheng ◽  
Zhiguo Zhang ◽  
...  
Keyword(s):  
Discrete Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
Output Measurement ◽  
Markov Jump Systems ◽  
Multiplicative Noises ◽  
Jump Systems

The singular systems, which could widely describe more general systems and present traits of physical features, are discussed in this study. Taking the fact that noises always exist in the state and output measurement of one singular system into consideration, which may cause some errors and decrease system performance, this article devotes itself to the dissipative control for discrete-time singular Markov jump systems (SMJSs) with multiplicative noises. To deal with the asynchronous phenomena between the system modes and the controller modes, a set of Markov chains are constructed. To make sure the closed-loop singular system is dissipative, a set of sufficient conditions are derived based on the linear matrix inequalities, and then the asynchronous controller is designed to ensure that SMJSs are stochastically admissible and strictly dissipative. Finally, a simulation example is carried out to verify the correctness of the derived theorem. The designed asynchronous controller improves the robustness of the controller and overcomes the asynchronous phenomenon. This control method can be applied in the fields of robot control system.

Stabilization of Discrete-Time Hidden Semi-Markov Jump Systems with Time-varying Emission Probability

2021 ◽  
Author(s):  
Shiyuan Fang ◽  
Hanzhi Li ◽  
Dacheng Pei ◽  
Meixi Wu ◽  
Yichong Sun ◽  
...  
Keyword(s):  
Discrete Time ◽  
Emission Probability ◽  
Time Varying ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Jump Systems
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