With an emphasis on a complete and totally self-contained presentation and containing an extensive (almost 400 entries) up-to-date bibliography and a detailed index, Mathematical Control Theory will be an excellent research reference source as well. The book covers the algebraic theory of linear systems, - including controllability, observability, feedback equivalence, families of systems, controlled invariant subspaces, realization, and minimality, - stability via Lyapunov as well as input/output methods, ideas of optimal control, observers and dynamic feedback, parameterization of stabilizing controllers, tracking, Kalman filtering (introduced through a deterministic version of "optimal observation"), and basic facts about frequency domain such as the Nyquist criterion.
Several nonlinear topics, such as Volterra series, smooth feedback stabilization, and finite-experiment observability, as well as many results in automata theory of relevance for discret-event control, are also included. The text highlights the distinctions and the similarities between continuous and discrete time systems, as well as the sampling process that relates them.

This textbook introduces the basic concepts and results of mathematical control and system theory. It is geared primarily to mathematically advanced undergraduate or beginning graduate students. It can also be used by engineering students interested in a rigorous, proof-oriented systems course.

Zusammenfassung
In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Inhalt
Series Preface * Preface to First Edition * 1 Introduction * 2 Systems * 3 Reachability and Controllability * 4 Nonlinear Controllability * 5 Feedback and Stabilization * 6 Outputs * 7 Observers and Dynamic Feedback * 8 Linear-Quadratic Optimal Control * 9 Time-Optimal Control of Linear Systems * 10 Remarks on Nonlinear Optimal Control * Appendixes * A Linear Algebra * B Differentials * C Ordinary Differential Equations * Bibliography * List of Symbols * Index