# American Institute of Mathematical Sciences

April  2016, 12(2): 471-486. doi: 10.3934/jimo.2016.12.471

## $p$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, China, China, China, China

Received  September 2014 Revised  February 2015 Published  June 2015

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.
Citation: Yi Zhang, Yuyun Zhao, Tao Xu, Xin Liu. $p$th Moment absolute exponential stability of stochastic control system with Markovian switching. Journal of Industrial & Management Optimization, 2016, 12 (2) : 471-486. doi: 10.3934/jimo.2016.12.471
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