  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
