Some necessary conditions for the exponential stability of one delay systems

Abstract

Some necessary conditions for the exponential stability of the one delay system are presented. In the case A1 is an invertible matrix, the condition depends exclusively on the Lyapunov matrix function of the delay system. The conditions are validated by examples for which the analytic characterization of the stability region is known.

Necessary conditions for the exponential stability of time-delay systems via the Lyapunov delay matrix

“…The results introduced in this section allow the reduction of the general functional v ( φ ) to a functional with a single delay, via the use of a transformation on the initial condition. This reduction is useful as it allows to extend straightforwardly the results on the single delay case obtained in . Moreover, it simplifies the proof as well as the notation.…”