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

Bin Zhou; Guang Ren Duan; Zongli Lin

doi:10.1109/ACC.2010.5530807

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

Bin Zhou^*
, Guang Ren Duan
, Zongli Lin

^*Corresponding author for this work

School of Astronautics

University of Virginia

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

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.

Original language	English
Title of host publication	Proceedings of the 2010 American Control Conference, ACC 2010
Publisher	IEEE Computer Society
Pages	4265-4270
Number of pages	6
ISBN (Print)	9781424474264
DOIs	https://doi.org/10.1109/ACC.2010.5530807
State	Published - 2010

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Name	Proceedings of the 2010 American Control Conference, ACC 2010

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10.1109/ACC.2010.5530807

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Zhou, B., Duan, G. R., & Lin, Z. (2010). A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 4265-4270). Article 5530807 (Proceedings of the 2010 American Control Conference, ACC 2010). IEEE Computer Society. https://doi.org/10.1109/ACC.2010.5530807

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

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.",

author = "Bin Zhou and Duan, \{Guang Ren\} and Zongli Lin",

year = "2010",

doi = "10.1109/ACC.2010.5530807",

language = "英语",

isbn = "9781424474264",

series = "Proceedings of the 2010 American Control Conference, ACC 2010",

publisher = "IEEE Computer Society",

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Zhou, B , Duan, GR & Lin, Z 2010, A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. in Proceedings of the 2010 American Control Conference, ACC 2010., 5530807, Proceedings of the 2010 American Control Conference, ACC 2010, IEEE Computer Society, pp. 4265-4270. https://doi.org/10.1109/ACC.2010.5530807

A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. / Zhou, Bin ; Duan, Guang Ren; Lin, Zongli.
Proceedings of the 2010 American Control Conference, ACC 2010. IEEE Computer Society, 2010. p. 4265-4270 5530807 (Proceedings of the 2010 American Control Conference, ACC 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

AB - 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.

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Zhou B , Duan GR, Lin Z. A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. In Proceedings of the 2010 American Control Conference, ACC 2010. IEEE Computer Society. 2010. p. 4265-4270. 5530807. (Proceedings of the 2010 American Control Conference, ACC 2010). doi: 10.1109/ACC.2010.5530807

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

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