An iterative method of Lyapunov function construction for differential inclusions
type: Item
instance of: scholarly article
title: An iterative method of Lyapunov function construction for differential inclusions
zbMATH Open document ID: 0628.34014
DOI: 10.1016/0167-6911(87)90085-5
author: V. A. Kamenetskiy
author: Eh. S. Pyatnitskij
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: The authors are concerned with sufficient conditions for the exponential stability of the zero solution of a differential inclusion of the form \(\dot x\in F(x)\), where \(x\in R^ n\), and F(x) denotes a set in \(R^ n\) of the form Ax where A is an \(n\times n\) matrix; this set F(x) is assumed to be the convex hull of a finite set of \(n\times n\) matrices \(A_ s\), \(s=1,...,M\). The conditions are in terms of positive definite quadratic Lyapunov functions which will exist with the required properties if a certain function of the matrix elements defining these Lyapunov functions and vectors in \(R^{nM}\) has a certain type of saddle point. A search algorithm for such saddle points is developed, as is an iterative algorithm for the construction of the Lyapunov function. An example and a generalization are also discussed.
reviewed by: G.Seifert
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4021628
zbMATH Keywords: differential inclusion
zbMATH Keywords: positive definite quadratic Lyapunov functions
zbMATH Keywords: saddle points
zbMATH Keywords: iterative algorithm
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90085-5
OpenAlex ID: W2064175629
cites work: On the application of Lyapunov's direct method to differential equations with ambiguous right sides
cites work: Q3266142
cites work: Q3335637
cites work: Numerical methods of Lyapunov function construction and their application to the absolute stability problem
description: scientific article; zbMATH DE number 4021628