Discrete-time modeling and stability analysis of periodic orbits with sliding for switched linear systems

Authors:
Yibo Zhao;Jiuchao Feng;Chi K. Tse
Affiliations:
School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China;School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China;Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong
Venue:
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Year:
2010

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Abstract

This paper establishes a discrete-time model and presents an exact method of stability analysis for periodic orbits containing a segment of sliding orbit for switched linear systems. Sliding dynamical equations are obtained by using Utkin's equivalent control method. Sliding mapping and impact mapping are obtained by solving the respective differential equations. A generalized discrete-time mapping for a cycle is derived for three operating scenarios. The coordinates of the periodic orbit points, inflow and outflow sliding regions, and the corresponding Jacobians are obtained. Theoretical analysis and simulation results for a third-order relay-feedback system and a second-order autonomous oscillating circuit are presented to illustrate the proposed model and method.