Mathematical Control Theory

§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.