Approximation of discrete-time systems with time-varying delay: Hankel norm criterion

The problem of Hankel norm model reduction for discrete-time systems with time-varying state delay is investigated. For a given stable system, this paper focuses on constructing stable reduced-order models under the Hankel norm error criterion. Two different approaches are proposed to solve this problem. One is based on the cone complementarity linearization idea, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints, and the other casts the model reduction into a convex optimization problem by using a linearization procedure. A numerical example is provided to show the effectiveness of the proposed theories.