Brief paper: A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation

Authors:
Bin Zhou;Guang-Ren Duan;Zongli Lin
Affiliations:
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin, 150001, China;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin, 150001, China;Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743-4743, Charlottesville, VA 22904-4743, USA
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

This paper is concerned with semi-global stabilization of discrete-time linear periodic systems subject to actuator saturation. Provided that the open loop characteristic multipliers are within the closed unit circle, a low gain feedback design approach is proposed to solve the problem by state feedback. Our approach is based on the solution to a parametric discrete-time periodic Lyapunov equation. The proposed approaches not only generalize the corresponding results for time-invariant systems to periodic systems, but also reveal some important intrinsic properties of this class of periodic matrix equations. A numerical example is worked out to illustrate the effectiveness of the proposed approaches.