Abstract
This paper considers the problem of stabilizing a linear time-invariant system with time delay
x(t)=A0x(t)+A1x(t-h)+Bu(t), h>0.
The object is to find a sufficient condition for the system to be stabilizable by means of linear feedback of x(t), i.e.,
u(t)=Kx(t).
The result is as follows. If (i) (A0, B) is a completely controllable pair and (ii) the columns of A1 can be represented as linear combinations of columns of B, then the degree of stability of the closed loop system can be specified arbitrarily.
The stabilizing feedback control law stated in this paper has the merit that the feedback can be constructed without the precise knowledge of the delay time (It is enough to know its upper bound).
