Mathematical Control Theory. Deterministic Finite Dimensional Systems
2nd edition

This textbook introduces the key concepts and results of Control and System Theory. Unique in its emphasis on foundational aspects, it is geared toward mathematically advanced undergraduate or graduate students. It is also suitable for a second engineering course in control, which goes beyond the classical frequency domain and state-space material. The choice of topics, together with detailed end-of-chapter links to the bibliography, makes this a useful research reference as well.
The book covers what constitutes the common core of control theory : the algebraic theory of linear systems, including controllability, observability, feedback equivalence, and minimality ; stability via Lyapunov, as well as input/output methods ; linear-quadratic optimal control ; observers and dynamic feedback ; Kalman filtering via deterministic optimal observation ; parametrization of stabilizing controllers, and basic facts about frequency domain such as the Nyquist criterion.
More advanced material has been added, or further elaborated upon, in this second edition, including : Lie-algebraic accessibility theory, feedback linearization, controllability of neural networks, Teachability under input constraints and time-optimal control for linear systems, basic topics in nonlinear feedback design (backstepping, damping, control-Lyapunov functions, topological obstructions to stabilization), and introductions to the calculus of variations, the maximum principle, and numerical optimal control.