Stability analysis of singular systems
type: Item
instance of: scholarly article
title: Stability analysis of singular systems
zbMATH Open document ID: 0688.93042
DOI: 10.1007/BF01598415
author: Mirko M. Milic
author: Vladimir B. Bajić
published in: Circuits, Systems, and Signal Processing
publication date: 1989-01-01T00:00:00Z
review text: This paper aims to outline a general stability theory based on the Lyapunov direct method for singular systems of the form (*) \(P(t,x)\dot x=f(t,x)\), where \(x\in {\mathbb{R}}^ n\) and \(f\in {\mathbb{R}}^ k\). Thus, P is in general a rectangular matrix and, when \(k=n\), P is allowed to be singular. In particular, (*) cannot be reduced in general to an usual state-space model. System (*) is considered under assumptions which ensure existence of solutions, but uniqueness is not assumed. This and other features of (*), cause the necessity of redefining in an appropriate way the classical notions of stability and asymptotic stability. A construction of a Lyapunov function candidate is presented.
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4128740
zbMATH Keywords: general stability theory
zbMATH Keywords: Lyapunov direct method
zbMATH Keywords: singular systems
zbMATH Keywords: asymptotic stability
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
Wikidata QID: Q57255501
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full work available at URL: https://doi.org/10.1007/bf01598415
OpenAlex ID: W2011891963
description: scientific article; zbMATH DE number 4128740