Extended H∞ filtering of Markov jump nonlinear systems with general uncertain transition probabilities

2015 ◽  
Vol 352 (11) ◽  
pp. 5269-5291 ◽  
Author(s):  
Mouquan Shen ◽  
Ju H. Park ◽  
Dan Ye
Keyword(s):  
Nonlinear Systems ◽  
Transition Probabilities ◽  
Markov Jump

scholarly journals Fuzzy-Model-Based Robust Control of Markov Jump Nonlinear Systems With Incomplete Transition Probabilities and Uncertain Packet Dropouts

2021 ◽  
Author(s):  
Zeyuan Xu ◽  
Meng Joo Er
Keyword(s):  
Nonlinear Systems ◽  
Transition Probabilities ◽  
Fuzzy Model ◽  
Mode Switching ◽  
Robot Arm ◽  
Markov Jump ◽  
Packet Dropouts ◽  
Complex Nonlinear Systems ◽  
Interval Type ◽  
System Mode

Abstract Interval type-2 fuzzy Markov jump systems (IT2FMJSs) have received much attention because they can better describe complex nonlinear systems with uncertainties and stochastic system mode switching. Over the past decade, many excellent results of fuzzy MJSs (FMJSs) have been reported. However, the transition probabilities which govern the dynamic behaviour of MJSs have been assumed to be completely known, limiting real-world applications of existing results. Different from the previous studies, transition probabilities between system modes switching are partly unknown, and packet dropouts of data transmission are uncertain in this study. The main contributions of this work are: (1) To analyze stochastic stability and reduce conservatism, a novel Lyapunov function which both depends on system mode and fuzzy basis function is constructed; (2) The existence of a mode-dependent and fuzzy-basis-dependent state-feedback controller is investigated; (3) The closedloop system is stochastically stable with a desired H∞ performance, thereby addressing the problem of incomplete transition probabilities and uncertain packet dropouts. An illustrative example of a robot arm is used to demonstrate the effectiveness and practicality of the proposed approach. By virtue of the proposed approach, the effects of incomplete transition probabilities and uncertain packet dropouts on IT2FMJSs are alleviated.

scholarly journals Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Ding Zhai ◽  
Liwei An ◽  
Jinghao Li ◽  
Qingling Zhang
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Feedback Controller ◽  
Sufficient Condition ◽  
Markov Jump ◽  
Stochastically Stable ◽  
Lyapunov Matrix ◽  
The Stability ◽  
Markov Jump Linear System

This paper is devoted to investigating the stability and stabilisation problems for discrete-time piecewise homogeneous Markov jump linear system with imperfect transition probabilities. A sufficient condition is derived to ensure the considered system to be stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent and variation-dependent state feedback controller is derived to guarantee the stochastic stability of the closed-loop system, and a new method is further proposed to design a static output feedback controller by introducing additional slack matrix variables to eliminate the equation constraint on Lyapunov matrix. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

T–S Fuzzy Control of Positive Markov Jump Nonlinear Systems

2018 ◽  
Vol 26 (4) ◽  
pp. 2374-2383 ◽  
Author(s):  
Jie Lian ◽  
Siyi Li ◽  
Jiao Liu
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Control ◽  
Markov Jump
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