Stability and L1-Gain Analysis of Periodic Piecewise Positive Systems with Constant Time Delay

Bohao Zhu; James Lam; Xiaochen Xie; Xiaoqi Song; Ka Wai Kwok

doi:10.1109/TAC.2021.3089640

Stability and L1-Gain Analysis of Periodic Piecewise Positive Systems with Constant Time Delay

Bohao Zhu
, James Lam
, Xiaochen Xie^*
, Xiaoqi Song
, Ka Wai Kwok^*

^*Corresponding author for this work

The University of Hong Kong

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

This article is concerned with the stability and L1-gain analysis of periodic piecewise positive systems with constant time delay. λ-exponential stability, which is applied to characterize the decay rates of the considered systems, is investigated first. A copositive Lyapunov-Krasovskii functional is used to obtain a sufficient stability condition. The stability condition characterizes the convergent speed of the state by the system matrices and the size of the time delay. One can also apply the Lyapunov-Krasovskii functional to characterize the L1-gain of the systems. By taking advantage of the periodic property of the system, linear inequalities are employed to characterize the L1-gain, and an unweighted upper bound of the L1-gain of the system is given.

Original language	English
Pages (from-to)	2655-2662
Number of pages	8
Journal	IEEE Transactions on Automatic Control
Volume	67
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2021.3089640
State	Published - 1 May 2022
Externally published	Yes

Keywords

L1-gain analysis
periodic systems
positive systems
stability analysis
time-delay systems

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10.1109/TAC.2021.3089640

Cite this

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title = "Stability and L1-Gain Analysis of Periodic Piecewise Positive Systems with Constant Time Delay",

abstract = "This article is concerned with the stability and L1-gain analysis of periodic piecewise positive systems with constant time delay. λ-exponential stability, which is applied to characterize the decay rates of the considered systems, is investigated first. A copositive Lyapunov-Krasovskii functional is used to obtain a sufficient stability condition. The stability condition characterizes the convergent speed of the state by the system matrices and the size of the time delay. One can also apply the Lyapunov-Krasovskii functional to characterize the L1-gain of the systems. By taking advantage of the periodic property of the system, linear inequalities are employed to characterize the L1-gain, and an unweighted upper bound of the L1-gain of the system is given.",

keywords = "L1-gain analysis, periodic systems, positive systems, stability analysis, time-delay systems",

author = "Bohao Zhu and James Lam and Xiaochen Xie and Xiaoqi Song and Kwok, \{Ka Wai\}",

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T1 - Stability and L1-Gain Analysis of Periodic Piecewise Positive Systems with Constant Time Delay

AU - Zhu, Bohao

AU - Lam, James

AU - Xie, Xiaochen

AU - Song, Xiaoqi

AU - Kwok, Ka Wai

PY - 2022/5/1

Y1 - 2022/5/1

N2 - This article is concerned with the stability and L1-gain analysis of periodic piecewise positive systems with constant time delay. λ-exponential stability, which is applied to characterize the decay rates of the considered systems, is investigated first. A copositive Lyapunov-Krasovskii functional is used to obtain a sufficient stability condition. The stability condition characterizes the convergent speed of the state by the system matrices and the size of the time delay. One can also apply the Lyapunov-Krasovskii functional to characterize the L1-gain of the systems. By taking advantage of the periodic property of the system, linear inequalities are employed to characterize the L1-gain, and an unweighted upper bound of the L1-gain of the system is given.

AB - This article is concerned with the stability and L1-gain analysis of periodic piecewise positive systems with constant time delay. λ-exponential stability, which is applied to characterize the decay rates of the considered systems, is investigated first. A copositive Lyapunov-Krasovskii functional is used to obtain a sufficient stability condition. The stability condition characterizes the convergent speed of the state by the system matrices and the size of the time delay. One can also apply the Lyapunov-Krasovskii functional to characterize the L1-gain of the systems. By taking advantage of the periodic property of the system, linear inequalities are employed to characterize the L1-gain, and an unweighted upper bound of the L1-gain of the system is given.

KW - L1-gain analysis

KW - periodic systems

KW - positive systems

KW - stability analysis

KW - time-delay systems

UR - https://www.scopus.com/pages/publications/85112215001

U2 - 10.1109/TAC.2021.3089640

DO - 10.1109/TAC.2021.3089640

M3 - 文章

AN - SCOPUS:85112215001

SN - 0018-9286

VL - 67

SP - 2655

EP - 2662

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 5

ER -

Stability and L1-Gain Analysis of Periodic Piecewise Positive Systems with Constant Time Delay

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Keywords

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