Differential and Integral Equations

Interval matrix systems---flow invariance and componentwise asymptotic stability

Octavian Pastravanu and Mihail Voicu

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Abstract

Given an interval matrix system with discrete- or continuous-time dynamics, the flow-invariance of a rectangular set with arbitrary time-dependence is introduced as a concept of geometric nature. A theorem for its characterization provides a link between the vector function describing the time-dependence of the rectangular set and a constant matrix, which, in a certain sense, dominates the interval matrix. For rectangular sets with exponential time-dependence, this link becomes a system of algebraic inequalities. If there exist flow-invariant rectangular sets approaching the state space origin for an infinite time horizon, then the interval matrix system exhibits two special types of asymptotic stability (called componentwise asymptotic stability - for arbitrarily time-dependent rectangular sets, and componentwise exponential asymptotic stability - for exponentially time-dependent rectangular sets), whose equivalence is proved. A necessary and sufficient condition for componentwise asymptotic stability is derived, which adequately exploits Schur or Hurwitz stability of the constant matrix dominating the interval matrix.

Article information

Source
Differential Integral Equations, Volume 15, Number 11 (2002), 1377-1394.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060728

Mathematical Reviews number (MathSciNet)
MR1920693

Zentralblatt MATH identifier
1028.34047

Subjects
Primary: 34D99: None of the above, but in this section
Secondary: 15A48 93D20: Asymptotic stability

Citation

Pastravanu, Octavian; Voicu, Mihail. Interval matrix systems---flow invariance and componentwise asymptotic stability. Differential Integral Equations 15 (2002), no. 11, 1377--1394. https://projecteuclid.org/euclid.die/1356060728


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