Characterization of Bounded Real Lemma for Commensurate Delay Systems

Bounded real lemma is discussed for commensurate delay systems, and a necessary and sufficient condition for the achievable H-infinity performance with respect to the interval delay is characterized by parameter-dependent LMIs. The condition is further transformed to standard LMIs, and it is shown that the parameter-region partitioning enables to treat the necessary and sufficient condition with arbitrary resolution and precision. The computation efficiency for the evaluation of optimal H-infinity performance is discussed with numerical examples. Copyright (c) 2024 The Authors.