Copyright © 2012 Yingqi Zhang 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

This paper addresses the problem of finite-time control via observer-based state feedback for a family of singular Markovian jump systems (SMJSs) with time-varying norm-bounded disturbance. Firstly, the concepts of singular stochastic finite-time boundedness and singular stochastic finite-time stabilization via observer-based state feedback are given. Then an observer-based state feedback controller is designed to ensure singular stochastic finite-time stabilization via observer-based state feedback of the resulting closed-loop error dynamic SMJS. Sufficient criteria are presented for the solvability of the problem, which can be reduced to a feasibility problem involving linear matrix inequalities with a fixed parameter. As an auxiliary result, we also discuss the problem of finite-time stabilization via observer-based state feedback of a class of SMJSs and give sufficient conditions of singular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs. Finally, illustrative examples are given to demonstrate the validity of the proposed techniques.