Homogeneous polynomial lyapunov functions for piecewise affine systems

Jun Xu Jun Xu,Lihua Xie Lihua Xie

doi:10.1109/acc.2005.1470019

Homogeneous polynomial lyapunov functions for piecewise affine systems

Jun Xu Jun Xu, Lihua Xie Lihua Xie

https://doi.org/10.1109/acc.2005.1470019

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Publication Date: Jun 8, 2005

Citations: 30

Affiliation: Nanyang Technological University

#Piecewise Affine Systems #Homogeneous Polynomial Lyapunov Functions + Show 8 more

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Abstract

This paper addresses the construction of piece-wise homogeneous polynomial Lyapunov functions (PHPLFs) for piecewise affine (PWA) systems. Sufficient conditions for the existence of PHPLFs of a given degree for both continuous-time and discrete-time PWA systems are obtained in terms of linear matrix inequalities (LMIs). The result contains existing results based on piecewise quadratic Lyapunov functions as special cases and provides a less conservative assertion of the stability of PWA systems, which is supported by numerical examples.

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