## Differential and Integral Equations

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

#### 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

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