# Spring 2024 - ECE 515

ECE 515 - Control System Theory and Design is a fundamental first-year graduate course on the modern theory of dynamical systems and control. It builds on an introductory undergraduate course in control (such as ECE 486) and emphasizes state-space techniques for the analysis of dynamical systems and the synthesis of control laws meeting given design specifications. Some familiarity with linear algebra, as well as ordinary differential equations, is strongly recommended, although the necessary material will be reviewed in the context of the course.

To register for the class go to the official listing.

Access the content & syllabus for the Spring 2024 offering using the links on the left. Demos require use of UIUC VPN.

## List of topics

Topics this course aims to cover are:

**System modeling and analysis**: system design as a control problem - constraints, goals and performance specifications, input-output and state space models; linearization; review of linear algebra; fundamentals of state-space analysis of linear systems**System structural properties**: stability; introduction to Lyapunov methods; controllability, observability; canonical forms and minimal realizations. Modeling uncertainties; system sensitivity and robustness measures.**Feedback system design**: basic properties of feedback; stabilization and eigenvalue placement by state and output feedback; disturbance rejection; observers for estimating states, and observer feedback systems**Optimum feedback control**: dynamic programming and the Hamilton-Jacobi-Bellman equation; synthesis of optimum state regulator systems; numerical methods**Introduction to the minimum principle**: calculus of variations and necessary conditions for optimal trajectories; minimum principle for bounded controls; time-optimal control of linear systems; numerical methods