On the stability of hybrid difference-differential systems
type: Item
instance of: scholarly article
title: On the stability of hybrid difference-differential systems
zbMATH Open document ID: 1183.34013
DOI: 10.1134/S0012266109050139
author: V. M. Marchenko
author: Jean-Jacques Loiseau
published in: Differential Equations
publication date: 2009-10-08T00:00:00Z
review text: Hybrid difference-differential systems are considered to include some class of neutral differential-difference equations after a suitable transformation. It is shown that the Cauchy problem for a class of hybrid systems has a unique solution. For systems with constant coefficients, \[ x_1'(t) = A_{11}x_1(t) + A_{12}x_2(t),\quad x_2(t) = A_{21}x_1(t) + A_{22}(t-h), \] it is proven that the system is asymptotically stable if and only if \(A_{22}\) is a Schur matrix and all characteristic roots of the system have negative real parts. Further, when the systen degenerates to a scalar equation, i.e. the matrices \(A_{ij}\) become numbers \(a_{ij}\), the above condition for asymptotic stability can be realised in terms of these coefficients.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34A38
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 5611080
zbMATH Keywords: Hybrid systems
zbMATH Keywords: differential-difference system
zbMATH Keywords: stability
MaRDI profile type: Publication
cites work: The reachability and observability of hybrid multirate sampling linear systems
cites work: Differential algebraic equations with after-effect
cites work: Stability of linear descriptor systems with delay: a Lyapunov-based approach
cites work: Neutral-type time-delay systems that are not formally stable are not BIBO stabilizable
cites work: Q4664616
cites work: Observability of the hybrid linear systems with constant coefficients
cites work: \(H_{\infty }\) and bibo stabilization of delay systems of neutral type
cites work: Q4831251
cites work: On the Observability of Linear Differential-Algebraic Systems With Delays
cites work: Representation of solutions of hybrid difference-differential systems
cites work: Linear stationary differential-algebraic systems: II. Relative controllability
cites work: Q5806127
cites work: Differential-difference equations
cites work: Introduction to functional differential equations
cites work: Q5293000
cites work: Über Differential-Differenzengleichungen mit anomalen Lösungen
cites work: A practical method for analyzing the stability of neutral type LTI-time delayed systems
full work available at URL: s0012266109050139
OpenAlex ID: W1973418858
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description: scientific article; zbMATH DE number 5611080