This is a collection of the lecture notes of the three authors for a first-year graduate course on control system theory and design (ECE 515 , formerly ECE 415) at the ECE Department of the University of Illinois at Urbana-Champaign. This is a fundamental course on the modern theory of dynamical systems and their control, and builds on a first-level course in control that emphasizes frequency-domain methods (such as the course ECE 486 , formerly ECE 386, at UIUC ). The emphasis in this graduate course is on state space techniques, and it encompasses modeling , analysis (of structural properties of systems, such as stability, controllability, and observability), synthesis (of observers/compensators and controllers) subject to design specifications, and optimization . Accordingly, this set of lecture notes is organized in four parts, with each part dealing with one of the issues identified above. Concentration is on linear systems , with nonlinear systems covered only in some specific contexts, such as stability and dynamic optimization. Both continuous-time and discrete-time systems are covered, with the former, however, in much greater depth than the latter. The main objective of this course is to teach the student some fundamental principles within a solid conceptual framework, that will enable her/him to design feedback loops compatible with the information available on the states of the system to be controlled, and by taking into account considerations such as stability, performance, energy conservation, and even robustness. A second objective is to familiarize her/him with the available modern computational, simulation, and general software tools that facilitate the design of effective feedback loops
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