STABILITY SWITCHES AND REVERSALS OF LINEAR SYSTEMS WITH COMMENSURATE DELAYS: A MATRIX PENCIL CHARACTERIZATION

Abstract This paper addresses the problem of asymptotic stability of linear time-delay systems including commensurate delays. More precisely we focus on the characterization of stability switches and reversals using a matrix pencil approach. The proposed approach makes use of the generalized eigenvalue distribution with respect to the unit circle of some appropriate finite-dimensional matrix pencils. Classical problems, as for example, hyperbolicity and delay-independent/delay-dependent stability characterizations are reconsidered, and simple computational conditions are derived.

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