Robustness of infinite dimensional systems

Abstract

The results contained within this thesis concern an abstract framework for a robustness analysis of exponential stability of infinite dimensional systems. The abstract analysis relies on the strong relationship between exponential stability and L2-stability which exists for many classes of linear systems. In Chapter 1a "stability radius", for systems governed by semigroups, is developed, for a class of "structured" perturbations of its generator. The abstract theory is illustrated by examples of perturbations of the boundary data for homogeneous boundary value problems and also perturbations arising due to neglected delay terms in differential delay equations. In Chapter 2a related problem of a non standard linear quadratic problem is studied, which leads to a stability analysis for certain nonlinear systems. In Chapter 3 an abstract L2-stability theory is developed and then applied to integrodifferential equations and time-varying systems, to investigate the robustness of exponential stability of such systems