Computation of quadratic cost functionals for linear systems with non-commensurate time delays

Abstract

A method of evaluating quadratic cost functional for linear systems with non-commensurate time delays is presented. The main computational tasks involved in the method include the solution of a symbolic Diaphontine equation by Euclidean algorithm and the factorization of a finite-degree polynomial. As compared with an existing general method, the proposed one is more efficient in computing cross-covariances or gradients of quadratic cost functionals with respect to a decision variable. An example illustrating the numerical implementation of the proposed method is presented.