The Infinite-Dimensional Standard and Strict Bounded Real Lemmas in Continuous Time: The Storage Function Approach

Abstract The bounded real lemma (BRL) is a classical result in systems theory, which provides linear matrix inequality criterium for dissipativity, via the Kalman-Yakubovich-Popov (KYP) inequality. BRL has many applications, among others $$H^\infty $$ H ∞ control. Extensions to infinite dimensional systems, although already present work of Yakubovich, have only been studied systematically last few decades. In this context various notions stability, observability and controllability exist, depending on hypothesis one may allow KYP-inequality unbounded solutions forces consider spatial form. paper we continuous time, dimensional, well-posed systems. Via an adaptation Willems’ storage function approach unified way address both standard strict forms BRL. We avoid making use Cayley transform time. While lemma, obtain analogous results as there exist discrete time case, when treating case additional conditions are required, at least stage. This might be caused by fact that does not preserve exponential important property transferring continuous-time system discrete-time system.