Stabilization for a class of second-order switched systems

Liguo Zhang; Yangzhou Chen; Pingyuan Cui

doi:10.1016/j.na.2005.03.082

Stabilization for a class of second-order switched systems

Liguo Zhang^*
, Yangzhou Chen
, Pingyuan Cui

^*Corresponding author for this work

Beijing University of Technology

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

26 Citations (Scopus)

Abstract

This paper considers the asymptotic stabilization problem of second-order linear time-invariant (LTI) autonomous switched systems consisting of two subsystems with unstable focus equilibrium. More precisely, we find a necessary and sufficient condition for the origin to be asymptotically stable under the predesigned switching law. The result is obtained without looking for a common Lyapunov function or multiple Lyapunov function, but studying the locus in which the two subsystem's vector fields are parallel. Then the "most stabilizing" switching laws are designed which have translated the switched system into a piecewise linear system. Two numerical examples are presented to show the potential of the proposed techniques.

Original language	English
Pages (from-to)	1527-1535
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	62
Issue number	8
DOIs	https://doi.org/10.1016/j.na.2005.03.082
Publication status	Published - 30 Sept 2005
Externally published	Yes

Keywords

Asymptotic stabilization
Switched systems
Switching law

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10.1016/j.na.2005.03.082

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AU - Zhang, Liguo

AU - Chen, Yangzhou

AU - Cui, Pingyuan

PY - 2005/9/30

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N2 - This paper considers the asymptotic stabilization problem of second-order linear time-invariant (LTI) autonomous switched systems consisting of two subsystems with unstable focus equilibrium. More precisely, we find a necessary and sufficient condition for the origin to be asymptotically stable under the predesigned switching law. The result is obtained without looking for a common Lyapunov function or multiple Lyapunov function, but studying the locus in which the two subsystem's vector fields are parallel. Then the "most stabilizing" switching laws are designed which have translated the switched system into a piecewise linear system. Two numerical examples are presented to show the potential of the proposed techniques.

AB - This paper considers the asymptotic stabilization problem of second-order linear time-invariant (LTI) autonomous switched systems consisting of two subsystems with unstable focus equilibrium. More precisely, we find a necessary and sufficient condition for the origin to be asymptotically stable under the predesigned switching law. The result is obtained without looking for a common Lyapunov function or multiple Lyapunov function, but studying the locus in which the two subsystem's vector fields are parallel. Then the "most stabilizing" switching laws are designed which have translated the switched system into a piecewise linear system. Two numerical examples are presented to show the potential of the proposed techniques.

KW - Asymptotic stabilization

KW - Switched systems

KW - Switching law

UR - https://www.scopus.com/pages/publications/24344486068

U2 - 10.1016/j.na.2005.03.082

DO - 10.1016/j.na.2005.03.082

M3 - Article

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SN - 0362-546X

VL - 62

SP - 1527

EP - 1535

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 8

ER -

Stabilization for a class of second-order switched systems

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Keywords

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