Balancing reduction of linear systems having multiple delays

Abstract

In this paper we apply the balancing reduction method to derive reduced‐order models for linear systems having multiple delays. The time‐domain balanced realization is achieved through computing the controllability and observability gramians in the frequency domain. With the variable transformation s = i tan(θ/2), the gramians of linear multi‐delay systems can be accurately evaluated by solving first‐order differential equations over a finite domain. The proposed approach is computationally superior to that of using the two‐dimensional realization of delay differential systems.