A General Integral Quadratic Constraints Theorem with Applications to a Class of Sampled-Data Systems

Abstract

In the framework of integral quadratic constraints a more general stability theorem is derived by relaxing the assumptions on the uncertainty. In contrast to existing results, input-output relations are only required to hold on a subspace of the full signal space. This result is employed to incorporate uncertainties exhibiting sampling behavior into the framework of integral quadratic constraints. The arising infinite dimensional stability test is exactly reduced to a finite dimensional linear matrix inequality. Advantages of this approach are illustrated for the specific case of an interconnection including a pulse-width modulator.