This book presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed and mathematically rigorous way.

The first volume is devoted to the state space analysis of dynamical systems with special emphasis on problems of uncertainty, whereas the second volume will be devoted to problems of control and measurement. The work combines features of a detailed introductory textbook with that of a reference source.

The first chapter of this volume is of an illustrative and motivational character. It presents a catalogue of dynamic models from six areas of application. The development of mathematical systems theory starts in Chapter 2 with an introduction to the state space description of dynamical systems. This introduction is followed by three substantial chapters on stability theory, perturbation theory and the analysis of uncertain systems. Special features are:

• a comprehensive treatment of Liapunov's stability theory,
• a detailed exposition of algebraic stability criteria,
• a presentation of classical perturbation theory for polynomials and matrices,
• a systematic introduction to μ-analysis,
• a development of spectral value sets as tools for the analysis of uncertain systems,
• an account of stability radii as robustness measures for various perturbation classes,
• a study of the transient behaviour of linear systems.