Quadratic stability of a class of switched nonlinear systems

Jun Zhao; Georgi M. Dimirovski

doi:10.1109/TAC.2004.825611

Quadratic stability of a class of switched nonlinear systems

Jun Zhao^*, Georgi M. Dimirovski

^*Corresponding author for this work

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

305 Citations (Scopus)

Abstract

Quadratic stability of a class of switched nonlinear systems is studied in this note. We first transform quadratic stability problem into an equivalent nonlinear programming problem. Then, we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using Karush-Kuhn-Tucker condition for nonlinear programming problems. The necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space, which is much easier to check.

Original language	English
Pages (from-to)	574-578
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	49
Issue number	4
DOIs	https://doi.org/10.1109/TAC.2004.825611
Publication status	Published - Apr 2004
Externally published	Yes

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abstract = "Quadratic stability of a class of switched nonlinear systems is studied in this note. We first transform quadratic stability problem into an equivalent nonlinear programming problem. Then, we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using Karush-Kuhn-Tucker condition for nonlinear programming problems. The necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space, which is much easier to check.",

keywords = "Completeness, Karush-Kuhn-Tucker (KKT) condition, Quadratic stability, Switched systems",

author = "Jun Zhao and Dimirovski, \{Georgi M.\}",

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AU - Dimirovski, Georgi M.

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AB - Quadratic stability of a class of switched nonlinear systems is studied in this note. We first transform quadratic stability problem into an equivalent nonlinear programming problem. Then, we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using Karush-Kuhn-Tucker condition for nonlinear programming problems. The necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space, which is much easier to check.

KW - Completeness

KW - Karush-Kuhn-Tucker (KKT) condition

KW - Quadratic stability

KW - Switched systems

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DO - 10.1109/TAC.2004.825611

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SP - 574

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

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ER -

Quadratic stability of a class of switched nonlinear systems

Abstract

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