Stabilization of Linear Systems with Delay

Abstract

This paper considers the problem of stabilizing a linear time-invariant system with delay x(t)=Ax(t)+Dx(t-h)+Bu(t), h>0 by means of a linear feedback without delay u(t)=Kx(t) to obtain a sufficient condition less restrictive than those obtained so far for such stabilization. The result is as follows. The system is stabilizable, if (i) (A, B) is a completely controllable pair, and (ii) when (A, B) is written in a Luenberger's canonical form, D=D₁+D₂ where the columns of D₁ are linear combinations of those of B and D₂ is a lower triangular matrix. The stabilization law stated in this paper is applicable even if the delay time h is not known precisely.