$p$th Moment absolute exponential stability of stochastic control system with Markovian switching

Yi  Zhang; Yuyun  Zhao; Tao  Xu; Xin  Liu

doi:10.3934/jimo.2016.12.471

Article Contents

2016, Volume 12, Issue 2: 471-486. Doi: 10.3934/jimo.2016.12.471

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$p$th Moment absolute exponential stability of stochastic control system with Markovian switching

1.
Department of Mathematics, College of Science, China University of Petroleum, Beijing 102249

Received: August 31, 2014

Revised: January 31, 2015

Published: March 2016

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Abstract

In this paper we discuss the $p$th moment absolute exponential stability of stochastic control system with Markovian switching. We first give a new concept of $p$th moment absolute exponential stability, then we establish some theorems under different hypotheses to guarantee the system $p$th moment absolutely exponentially stable. These sufficient conditions in our theorems are algebraic criteria in terms of matrix inequalities, and we introduce an $M$-method with MATLAB to compute them. Finally, some examples are given to illustrate our results.

Keywords:

Absolute stability,
$p$th moment absolute exponential stability,
stochastic control systems,
stochastic differential equation,
Markovian switching.

Mathematics Subject Classification: Primary: 60H10, 34F05, 93E03, 93E15; Secondary: 60J27, 60G17.

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