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

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171 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	885-890
页数	6
期刊	IEEE Transactions on Automatic Control
卷	48
期	5
DOI	https://doi.org/10.1109/TAC.2003.811274
出版状态	已出版 - 5月 2003
已对外发布	是

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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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On quadratic Lyapunov functions

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