Stability of Linear Difference and Differential Inclusions

Authors:
P. Diamond;V. I. Opoitsev
Affiliations:
University of Queensland, Brisbane, Australia;University of Queensland, Brisbane, Australia
Venue:
Automation and Remote Control
Year:
2001

Citing 2
Cited 0

Matrix analysis

Matrix analysis
Criteria of asymptotic stability of differential and difference inclusions encountered in control theory

Systems & Control Letters

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Abstract

Any given in×in matrix iA is shown to be a restriction, to the iA-invariant subspace, of a nonnegative iN×iN matrix iB of spectral radius ρ(iB) arbitrarily close to ρ(iA). A difference inclusion x^{k+1}\in\mathbb{A} x^{k}, where \mathbb{A} is a compact set of matrices, is asymptotically stable if and only if \mathbb{A} can be extended to a set \mathbb{B} of nonnegative matrices iB with \|B\|_{1} or \|B\|_{\infty}. Similar results are derived for differential inclusions.