Discretization of continuous systems with internal and external point delays through a quasiparametrical ARMA model

Abstract

In this note, a discrete input/output model, which involves an ARMA part plus a nonrecursive additive term associated with the initial conditions of the free response, is formulated for continuous linear time-invariant systems involving internal and external point delays. The model is obtained from the application of the Cayley-Hamilton theorem to the continuous state-transition matrix. In some particular situations of asymptotic stability of the free system, the additive term associated with the response to initial conditions tends to a constant as time increases to infinity, and can be compensated through feedback so that the closed-loop model becomes a classical ARMA model