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2002 Interval matrix systems---flow invariance and componentwise asymptotic stability
Octavian Pastravanu, Mihail Voicu
Differential Integral Equations 15(11): 1377-1394 (2002).

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.

Citation

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Octavian Pastravanu. Mihail Voicu. "Interval matrix systems---flow invariance and componentwise asymptotic stability." Differential Integral Equations 15 (11) 1377 - 1394, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1028.34047
MathSciNet: MR1920693

Subjects:
Primary: 34D99
Secondary: 15A48 , 93D20

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 11 • 2002
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