Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 897481, 15 pages
Research Article

Stochastic Finite-Time Control of Discrete-Time Systems with Packet Loss

1College of Science, Henan University of Technology, Zhengzhou 450001, China
2Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China

Received 26 August 2011; Revised 13 December 2011; Accepted 18 December 2011

Academic Editor: Zhan Shu

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.


This paper investigates the stochastic finite-time stabilization and control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic finite-time boundedness and then state feedback controllers are designed to guarantee stochastic finite-time stabilization of the class of stochastic systems. The stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.