Abstract
This paper is concerned with the problem of stablizing a linear time-invariant system with time delay described by the differential-difference equation
S0: {x(t)=Ax(t)+Dx(t-h)+Bu(t), t≥0 x(t)=φ(t), t∈[-h, 0]
by means of a linear feedback without delay
u(t)=KTx(t)
Such a stabilization problem has been studied by many researchers and some sufficient conditions for S0 to be able to stabilized by the linear feedback has been derived. Classes of the system satisfing these conditions, however, seem to be restrictive considerably. The purpose of this paper is to broaden the class.
The obtained stabilizability condition is given as the structure of the matrix D to be satisfied when (A, B) is represented in Luenberger's cannonical form, which can give the same result as previous one as a special case.
The stabilization method provided here is applicable without knowledge the precise value of delay time.
