Stabilization and <italic>L</italic>&#x2082;&#x2013; Gain Performance of Periodic Piecewise Impulsive Linear Systems

Yongzhuang Liu; Yang Song; Haibo Qu; Zhi Chen

doi:10.1109/ACCESS.2020.3035024

IEEE Access (Jan 2020)

Stabilization and <italic>L</italic>₂– Gain Performance of Periodic Piecewise Impulsive Linear Systems

Yongzhuang Liu,
Yang Song,
Haibo Qu,
Zhi Chen

Affiliations

Yongzhuang Liu: ORCiD; Department of Automation, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China
Yang Song: ORCiD; Department of Automation, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China
Haibo Qu: ORCiD; Department of Automation, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China
Zhi Chen: ORCiD; Department of Automation, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China

DOI: https://doi.org/10.1109/ACCESS.2020.3035024
Journal volume & issue: Vol. 8
pp. 200146 – 200156

Abstract

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This paper deals with the stability, stabilization and L2- gain problem of periodic piecewise impulsive linear system. Firstly, by developing a new Lyapunov function called multiple piecewise time-varying Lyapunov function, a sufficient condition that guarantee the system λ* - exponentially stable is established. Moreover, a state-feedback controller is designed to stabilize the system. Then L2- gain analysis is investigated to obtain a result that guarantee the system λ* - exponentially stable and with L2- gain performance. Finally, numerical simulation examples are provided to verify the effectiveness of the results proposed in this paper.

Published in IEEE Access

ISSN: 2169-3536 (Online)
Publisher: IEEE
Country of publisher: United States
LCC subjects: Technology: Electrical engineering. Electronics. Nuclear engineering
Website: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

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