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Mathematical Problems in Engineering
Volume 2017, Article ID 7057628, 13 pages
https://doi.org/10.1155/2017/7057628
Research Article

Disordered Stabilization of Stochastic Delay Systems: The Disorder-Dependent Approach

School of Information and Control Engineering, Liaoning Shihua University, Fushun, Liaoning 113001, China

Correspondence should be addressed to Guoliang Wang; moc.nuyila@gnawgnailg

Received 20 December 2016; Accepted 16 February 2017; Published 20 March 2017

Academic Editor: Sabri Arik

Copyright © 2017 Guoliang Wang and Hongyang Cai. 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

In this paper, a general stabilization problem of stochastic delay systems is realized by a disordered controller and studied by exploiting the disorder-dependent approach. Different from the traditional results, the stabilizing controller here experiences a disorder between control gains and system states. Firstly, the above disorder is described by the robust method, whose probability distribution is embodied by a Markov process with two modes. Based on this description, a kind of disordered controller having special uncertainties and depending on a Markov process is proposed. Then, by exploiting a disorder-dependent Lyapunov functional, two respective conditions for the existence of such a disordered controller are provided with LMIs. Moreover, the presented results are further extended to a general case that the corresponding transition rate matrix of the disordered controller has uncertainties. Finally, a numerical example is exploited to demonstrate the effectiveness and superiority of the proposed methods.