On quadratic Lyapunov functions

Daizhan Cheng; Lei Quo; Jie Huang

doi:10.1109/TAC.2003.811274

On quadratic Lyapunov functions

Daizhan Cheng, Lei Quo, Jie Huang

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

171 Scopus citations

Abstract

A topological structure, as a subset of [0, 2π)^L × ℝ₊^n-11, is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral. The structure and the conditions are considerably simplified for planar systems. It is also proved that a set of block upper triangular matrices share a common QLF, iff each set of diagonal blocks share a common QLF.

Original language	English
Pages (from-to)	885-890
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	48
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2003.811274
State	Published - May 2003
Externally published	Yes

Keywords

Common quadratic Lyapunov function (QLF)
Stabilization
Switched system

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10.1109/TAC.2003.811274

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AU - Quo, Lei

AU - Huang, Jie

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AB - A topological structure, as a subset of [0, 2π)L × ℝ+n-11, is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral. The structure and the conditions are considerably simplified for planar systems. It is also proved that a set of block upper triangular matrices share a common QLF, iff each set of diagonal blocks share a common QLF.

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KW - Switched system

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On quadratic Lyapunov functions

Abstract

Keywords

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