Stability robustness analysis of linear systems

Abstract

In this thesis, robustness of stability of linear, time-invariant, continuousand discrete-time systems is investigated. Only state-space models and additive perturbations are considered. Existing results concerning stability robustness of continuous-time systems, based on Liapunov approach and continuity of eigenvalues, are reviewed; and similar results for discretetime systems under single- and multi-parameter additive jDerturbations are derived. An inherent difficulty which originates from mixed linear and bilinear appearance of perturbation parameters in inequalities defining robustness regions of discrete-time systems is resolved by transforming the problem to robustness of a higher order continuous-time system. Finally, stability robustness of discrete-time interconnected systems is studied, and various approaches are compared.