On quadratic Liapunov functionals for linear difference equations
type: Item
instance of: scholarly article
title: On quadratic Liapunov functionals for linear difference equations
zbMATH Open document ID: 0851.39006
DOI: 10.1016/0024-3795(94)00183-9
author: L. A. V. Carvalho
published in: Linear Algebra and its Applications
publication date: 1996-06-30T00:00:00Z
review text: By means of a quadratic Lyapunov functional defined in an appropriate \(L_2\) space, the author studies some stability properties of vector linear difference equations of the form \[ x(t)= \sum^k_{j=1} A_j x(t- r_j), \qquad 0< r_1< r_2< \dots< r_k< \infty, \] where \(A_j\), \(j=1, 2, \dots, k\) are given \(N\times N\) real matrices. In particular, the author gives a criterion which determines stability with respect to the delays \(r_j\). For related results see the papers of \textit{J. Hurt} [SIAM J. Numer. Anal. 4, 582-596 (1967; Zbl 0264.65076)] and \textit{W. R. Melvin} [J. Math. Anal. Appl. 48, 749-763 (1974; Zbl 0311.39002)].
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 894234
zbMATH Keywords: quadratic Lyapunov functional
zbMATH Keywords: stability
zbMATH Keywords: vector linear difference equations
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00183-9
OpenAlex ID: W2153772638
cites work: Q4065362
cites work: On a new extension of Liapunov’s direct method to discrete equations
cites work: Q5579577
cites work: Q5584128
cites work: Some Stability Theorems for Ordinary Difference Equations
cites work: Stability properties of functional difference equations
cites work: On the discrete-time bounded real lemma with application in the characterization of static state feedback \(H_ \infty\) controllers
cites work: Dynamical systems and evolution equations. Theory and applications
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description: scientific article; zbMATH DE number 894234