Finite frequency approaches to H∞ model reduction for continuous-time state delayed systems

This paper discusses the H_∞ model reduction problem for linear continuous-time systems with pure state delay. Different from the conventional entire-frequency H_∞ approximation performance specification, finite-frequency H_∞ norm was adopted in this paper, which is a more suitable index to characterize the model reduction problems for systems with apriori known operating frequency range. Based on the recently developed TDS GKYP (time delay system Generalized Kalman-Yakubovich-Popov) lemma, sufficient conditions for the finite frequency H_∞ model reduction problems are derived and expressed in terms of solutions to a set of linear matrix inequalities (LMIs). Numerical example was included for illustration.