Abstract
This paper considers the problem of stabilizing a linear time-invariant system with delay of retarded type x(t)=Ax(t)+Dx(t-h)+Bu(t), h>0, by means of a linear feedback Without delay u(t)=Kx(t).
The object is 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 canonical form of Popov or Luenberger, and D is divided by a certain rule, the norms of those parts of D satisfy a certain inequality.
In the previous results on this problem the restriction of the structure of coefficient matrix D has been put in the stabilizability condition. However, the constraint on the structure of the matrix is completely removed in this result.
