Linear Dynamic Systems

4 units · Graduate courses (200-299)

(Formerly numbered M240A.) Lecture, four hours; outside study, eight hours. Preparation: advanced linear algebra and mathematical maturity. Study of linear time-invariant (LTI) and time-varying (LTV) systems in continuous and discrete time using state-space descriptions. Analysis of state equations and its solutions. Introduction to the concepts of controllability, observability, normal forms for LTI systems and relation to feedback invariants. Discussion of stability for nonlinear differential equations and its characterization through Lyapunov functions for LTV systems and eigenvalues for LTI systems. Design of stabilizing controllers through state feedback and observers, and discussion of the separation principle. Introduction to system identification. Letter grading.