Computation of the state transition matrix for a class of delay-differential systems†

Abstract

Systems which can be modelled by a linear constant coefficient delay-differential equation of the form [xdot](t) = A0x(t) + A1,.x(t— h) are studied, where,x(r)∊Rn is the instantaneous state at time t, h > 0 is the delay and matrices A0 and A1 are of appropriate dimensions. A method for the computation of the state transition matrix in the closed form for this class of systems is given. We then analyse the form of the State transition matrix for the delay-differential systems with finite spectrum. Finally, the problem of pointwise degeneracy for such systems is discussed.