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Mathematical Problems in Engineering
Volume 2014, Article ID 769302, 6 pages
http://dx.doi.org/10.1155/2014/769302
Research Article

Spectral Perspective on the Stability of Discrete-Time Markov Jump Systems with Multiplicative Noise

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China

Received 30 April 2014; Accepted 28 June 2014; Published 10 July 2014

Academic Editor: Quanxin Zhu

Copyright © 2014 Ting Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We apply the spectrum analysis approach to address the stability of discrete-time Markov jump systems with state-multiplicative noise. In terms of the spectral distribution of a generalized Lyapunov operator, spectral criteria are presented to testify three different kinds of stochastic stabilities: asymptotic mean square stability, critical stability, and essential instability.