Pointwise Stabilization of Discrete-time Stationary Matrix-valued Markovian Chains

2011/07/01 by Dai, Xiongping, Huang, Yu, Xiao, Mingqing
#37N35 #61J10 #93A30 #93C05 #93D20 #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1107.0132

Abstract

We study the pointwise stabilizability of a discrete-time, time-homogeneous, and stationary Markovian jump linear system. By using measure theory, ergodic theory and a splitting theorem of state space we show in a relatively simple way that if the system is essentially product-bounded, then it is pointwise convergent if and only if it is pointwise exponentially convergent.

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