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Mathematical Problems in Engineering
Volume 2013, Article ID 931695, 9 pages
http://dx.doi.org/10.1155/2013/931695
Research Article

Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China

Received 18 January 2013; Revised 13 March 2013; Accepted 18 March 2013

Academic Editor: Rongni Yang

Copyright © 2013 Zhongwei Lin 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 investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree set . Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.