Stability of polytopic systems via convex \(M\)-matrices and parameter-dependent Lyapunov functions
type: Item
instance of: scholarly article
title: Stability of polytopic systems via convex \(M\)-matrices and parameter-dependent Lyapunov functions
zbMATH Open document ID: 0955.34040
DOI: 10.1016/S0362-546X(00)85036-1
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-02-21T00:00:00Z
review text: The authors are interested in the set \({\mathbf M}_n\) of \(M\)-matrices. They are matrices whose off diagonal elements are nonpositive, and whose eigenvalues have positive real parts. It is well known that in general the sum or a convex combination of \(M\)-matrices is not an \(M\)-matrix. The main objective of the paper is to derive a number of sufficient conditions which can be used to check that all the matrices of a polytope are \(M\)-matrices, by testing only the vertices. The results are applied to the stability problem of uncertain linear and nonlinear systems.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 93C41
zbMATH DE Number: 1472239
zbMATH Keywords: \(M\)-matrices
zbMATH Keywords: uncertain systems
zbMATH Keywords: stability
author: Dušan M. Stipanović
author: Dragoslav D. Siljak
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
cites work: Q4070950
cites work: Q5485394
cites work: Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis
cites work: Q3943082
cites work: Comments regarding "On stability of interval matrices" [with reply]
cites work: Linear Matrix Inequalities in System and Control Theory
cites work: Q5340130
cites work: New conditions for global stability of neural networks with application to linear and quadratic programming problems
cites work: Affine parameter-dependent Lyapunov functions and real parametric uncertainty
cites work: Q3901357
cites work: Q5584086
cites work: Q4040931
cites work: Regulators for linear, time invariant plants with uncertain parameters
cites work: Lotka-Volterra equations: Decomposition, stability, and structure. Part I: Equilibrium analysis
cites work: Q3975393
cites work: Cellular systems. II: Stability of compartmental systems
cites work: Q4284052
cites work: Q3999518
cites work: Q4099452
cites work: $L_2 $-Stability and -Instability of Large-Scale Systems Described by Integrodifferential Equations
cites work: An extension of the Levy-Desplanque theorem and some stability conditions for matrices with uncertain entries
cites work: A Lyapunov function for some naturally-occurring linear homogeneous time-dependent equations
cites work: On stability of interval matrices
cites work: Explicit formulas for stability radii of nonnegative and Metzlerian matrices
cites work: Connective stability of competitive equilibrium
cites work: Q4160745
full work available at URL: s0362-546x(00)85036-1
OpenAlex ID: W2063900886
description: scientific article; zbMATH DE number 1472239