Mathematical control theory is a separate branch of mathematics that has, over a span of 150 years, developed an extensive literature covering its various ideas and applications. This text presents basic concepts and results in the field. It requires only a knowledge of basic facts from linear algebra, differential equations and calculus, with a few more concepts required for the final part of the book. In addition to classical concepts and ideas, the book presents many recently published results. It explains impulsive control, positive systems, stabilization of nonlinear systems, control of rigid bodies, stabilization of infinite dimensional systems and the minimum energy problem. The book should be useful for a beginning graduate course in mathematical control theory or for self study by professionals needing a complete picture of the mathematics that underly the applications of control theory.

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