Advances in Difference Equations
Volume 2009 (2009), Article ID 896218, 23 pages
doi:10.1155/2009/896218
Research Article

Switching Controller Design for a Class of Markovian Jump Nonlinear Systems Using Stochastic Small-Gain Theorem

Jin Zhu,1 Junhong Park,1 Kwan-Soo Lee,1 and Maksym Spiryagin2

1Department of Mechanical Engineering, Hanyang University, 133-791 Seoul, South Korea
2Dipartimento di Meccanica, Politecnico di Torino, 10129 Torino, Italy

Received 2 October 2008; Revised 24 December 2008; Accepted 16 January 2009

Academic Editor: Leonid Shaikhet

Copyright © 2009 Jin Zhu 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

Switching controller design for a class of Markovian jump nonlinear systems with unmodeled dynamics is considered in this paper. Based on the differential equation and infinitesimal generator of jump systems, the concept of Jump Input-to-State practical Stability (JISpS) in probability and stochastic Lyapunov stability criterion are put forward. By using backsetpping technology and stochastic small-gain theorem, a switching controller is proposed which ensures JISpS in probability for the jump nonlinear system. A simulation example illustrates the validity of this design.