Complete characterization of quadratic Lyapunov functions for planar systems in LMI regions

Dongmei Xie Dongmei Xie,Guangming Xie Guangming Xie,Long Wang Long Wang

doi:10.1109/acc.2003.1240542

Complete characterization of quadratic Lyapunov functions for planar systems in LMI regions

Dongmei Xie Dongmei Xie, Guangming Xie Guangming Xie + Show 1 more

https://doi.org/10.1109/acc.2003.1240542

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Publication Date: Jun 4, 2003

Affiliation: Peking University

#Linear Matrix Inequality Region #Common Quadratic Lyapunov Function + Show 8 more

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Abstract

This paper discusses the problem of finding a common quadratic Lyapunov function (CQLF) for planar systems in linear matrix inequality (LMI) regions. The main contribution of this paper is to give a complete characterization of quadratic Lyapunov functions (QLFs) for a given planar system, which is stable in an LMI region, and obtain a necessary and sufficient condition for such a class of planar systems to share a CQLF in the LMI region. The results are not only verifiable but also constructive, which can be realized by computer easily.

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