H∞ Control for Discrete-time Nonhomogeneous Markov Jump Linear System with Partly Accessed Transition Rates

2019 ◽  
Author(s):  
Jiawei Shan ◽  
Mingang Hua ◽  
Juntao Fei
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Transition Rates ◽  
Markov Jump ◽  
Markov Jump Linear System

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.

A BRL for A Class of Discrete-time Markov Jump Linear System with Piecewise-Constant TPs

2011 ◽  
Vol 44 (1) ◽  
pp. 8699-8704 ◽  
Author(s):  
Lixian Zhang ◽  
Yu Leng ◽  
Lingjie Chen ◽  
Ye Zhao
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Markov Jump ◽  
Piecewise Constant ◽  
Markov Jump Linear System

scholarly journals RobustH∞Filtering for Discrete-Time Markov Jump Linear System with Missing Measurements

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yingjun Niu ◽  
Wei Dong ◽  
Yindong Ji
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Missing Measurements ◽  
Markov Jump ◽  
Stochastically Stable ◽  
Error System ◽  
Markov Jump Linear System

The problem of robustH∞filtering is investigated for discrete-time Markov jump linear system (DMJLS) with uncertain parameters and missing measurements. The missing measurements process is modelled as a Bernoulli distributed sequence. A robustH∞filter is designed and sufficient conditions are established in terms of linear matrix inequalities via a mode-dependent Lyapunov function approach, such that, for all admissible uncertain parameters and missing measurements, the resulting filtering error system is robustly stochastically stable and a guaranteedH∞performance constraint is achieved. Furthermore, the optimalH∞performance index is subsequently obtained by solving a convex optimisation problem and the missing measurements effects on theH∞performance are evaluated. A numerical example is given to illustrate the feasibility and effectiveness of the proposed filter.

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