Common Lyapunov function based on Kullback-Leibler divergence for a switched nonlinear system
type: Item
instance of: scholarly article
title: Common Lyapunov function based on Kullback-Leibler divergence for a switched nonlinear system
zbMATH Open document ID: 1213.93168
DOI: 10.1155/2011/723509
author: Omar M. Abou Al-Ola
author: Ken'ichi Fujimoto
author: Tetsuya Yoshinaga
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/222844
review text: Summary: Many problems with control theory have led to investigations into switched systems. One of the most urgent problems related to the analysis of the dynamics of switched systems is the stability problem. The stability of a switched system can be ensured by a common Lyapunov function for all switching modes under an arbitrary switching law. Finding a common Lyapunov function is still an interesting and challenging problem. The purpose of the present paper is to prove the stability of equilibrium in a certain class of nonlinear switched systems by introducing a common Lyapunov function; the Lyapunov function is based on generalized Kullback-Leibler divergence or Csiszár's \(I\)-divergence between the state and equilibrium. The switched system is useful for finding positive solutions to linear algebraic equations, which minimize the I-divergence measure under arbitrary switching. One application of the stability of a given switched system is in developing a new approach to reconstructing tomographic images, but nonetheless, the presented results can be used in numerous other areas.
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 5904915
Wikidata QID: Q58693391
MaRDI profile type: Publication
OpenAlex ID: W2011436546
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description: scientific article; zbMATH DE number 5904915