Constrained approximation of multiple input–output delay systems using genetic algorithm

The paper presents a constrained H 2 approximation method for multiple input–output delay systems by using a genetic algorithm. The H 2 error between the original and the approximate models is minimized subject to constraints on the H ∞ error between them and the matching of their steady-state under step inputs. In particular, the H 2 error is used as the objective (fitness) function for minimization with the best parameters of the approximate model obtained by repeating the genetic operations on the population incorporated a parameter search space expansion scheme. The effectiveness of the proposed method is demonstrated by numerical examples. It is shown that the approximate models obtained by this approach have better approximation performance in both the H 2 and H ∞ norms, as well as the steady-state response, than those obtained by a previous gradient-based minimization approach.