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

• Published in: Automatica (Oxford) Vol. 47; no. 2; pp. 316 - 325
• Main Authors: Zhou, Bin, Duan, Guang-Ren, Lin, Zongli
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.02.2011; Elsevier
• Subjects: Actuator saturation; Actuators; Applied sciences; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Design engineering; Exact sciences and technology; Gain; Mathematical analysis; Mathematical models; Parametric periodic Lyapunov equation; Periodic systems; Saturation; Semi-global stabilization; Stabilization; State feedback; Semi-global stabilization; Parametric periodic Lyapunov equation; Periodic systems; Actuator saturation; State feedback; Operator equation; Saturation; Unit circle; Control synthesis; Lyapunov equation; Global stabilization; Discrete time; Small gain theorem; Open loop; Multiplier; Invarying system; Matrix equation; Periodic system; Actuator
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2010.10.011

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.