SUFFICIENCY-TYPE CONDITIONS FOR A TYPE OF STRICTLY DECREASING SOLUTIONS OF LINEAR CONTINUOUS-TIME DIFFERENTIAL SYSTEMS WITH BOUNDED POINT TIME-VARYING DELAYS

Manuel De la Sen

Manuel De la Sen UPV/EHU), Leioa 48940, Bizkaia, Spain

Article ID: 2440

Keywords: time-delay system, time-delay function, bounded time-varying delays, zero-delay system

Abstract

This paper investigates sufficiency-type conditions for strictly decreasing solutions of linear time-delay differential systems subject to a finite number of time-varying bounded point delays. The delay functions are not required to be time-differentiable nor even continuous but simply piecewise bounded continuous. It is not also required for the delay functions at any time instant to be upper-bounded. It is not necessary to have the knowledge of either the delay functions or their lower and upper bounds. It is proved that the supremum of any vector norm of the solution trajectory on consecutive time intervals of finite lengths is strictly decreasing under either stability conditions on the matrix which describes the delay-free dynamics, or on the one which describes the zero-delay auxiliary system, provided in both cases the contribution of the delayed dynamics is sufficiently small related to the convergence abscissas of the above matrices.

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