Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

2008 ◽  
Vol 26 (3) ◽  
pp. 495-525 ◽  
Author(s):  
Vasile Dragan ◽  
Toader Morozan
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
General Class ◽  
Stochastic Systems ◽  
Mean Square ◽  
Linear Stochastic Systems ◽  
Stability In Mean Square ◽  
Time Linear

scholarly journals Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yueying Liu ◽  
Ting Hou
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Mean Square ◽  
Markov Jump ◽  
Multiplicative Noises ◽  
Exogenous Disturbance ◽  
Mean Square Exponential Stability

In this paper, exponential stability and robust H∞ control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises. The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovskii functional, a new sufficient condition in terms of matrix inequalities is derived to guarantee the mean square exponential stability of the equilibrium point. Then some sufficient conditions for the existence of feedback controller are presented to guarantee that the resulting closed-loop system has mean square exponential stability for the zero exogenous disturbance and satisfies a prescribed H∞ performance level. Numerical simulations are exploited to validate the applicability of developed theoretical results.

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