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

Zhongwei Lin,Jizhen Liu,Yuguang Niu

doi:10.1155/2013/931695

Zhongwei Lin, Jizhen Liu + Show 1 more

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https://doi.org/10.1155/2013/931695

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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 setn,…,n. 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.

Highlights

Markovian jump systems have been studied since the pioneering work on quadratic control of linear jump systems in the 1960s
This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems
Motivated by the nonlinear control theory for the deterministic systems, we present the following definition related to the relative degree for Markovian jump nonlinear systems

Summary

Introduction

Markovian jump systems have been studied since the pioneering work on quadratic control of linear jump systems in the 1960s. Reference [7] has investigated the problem of control for discrete time-delay linear systems with Markovian jump parameters. References [10, 11] discussed the sliding mode control problems for Markovian jump linear singular systems. Reference [20] has discussed the stabilization problem for a class of Markovian jump nonlinear systems in the special canonical form. This paper investigates the linearization and stabilizing control design problems for Markovian jump nonlinear systems. According to the proposed relative degree set definition, the appropriate coordinate is adopted under which the system can be transformed into the canonical form followed with the Markovian switchings.

Feedback Linearization

Stabilizing Control Design

Simulation Results

Conclusion