Stability analysis of discrete-time Markov jump linear singular systems with partially known transition probabilities

2021 ◽  
Vol 158 ◽  
pp. 105057
Author(s):  
Jorge C. Guerrero ◽  
Jorge R. Chávez-Fuentes ◽  
Juan E. Casavilca ◽  
Eduardo F. Costa
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Markov Jump

Regularity and stability analysis of discrete-time Markov jump linear singular systems

Automatica ◽  
2017 ◽  
Vol 76 ◽  
pp. 32-40 ◽  
Author(s):  
Jorge R. Chávez-Fuentes ◽  
Eduardo F. Costa ◽  
Jorge E. Mayta ◽  
Marco H. Terra
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Singular Systems ◽  
Markov Jump

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.

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