EE 8215 – Nonlinear Systems
Mihailo Jovanovic, University of Minnesota, Spring 2013
Introduction. Examples of nonlinear systems. State-space models. Equilibrium points. Linearization. Range of nonlinear phenomena: finite escape time, multiple isolated equilibria, limit cycles, chaos. Bifurcations. Phase portraits. Bendixson and Poincare-Bendixson criteria. Mathematical background: existence and uniqueness of solutions, continuous dependence on initial conditions and parameters, normed linear spaces, comparison principle, Bellman-Gronwall Lemma. Lyapunov stability. Lyapunov's direct method. Lyapunov functions. LaSalle's invariance principle. Estimating region of attraction. Center manifold theory. Stability of time-varying systems. Input-output and input-to-state stability. Small gain theorem. Passivity. Circle and Popov criteria for absolute stability. Perturbation theory and averaging. Singular perturbations. Feedback and input-output linearization. Zero dynamics. Backstepping design. Control Lyapunov functions.
TuTh, 2:30pm - 3:45pm, Keller Hall 3-125; Jan 22 - May 10, 2013
Instructor and Teaching Assistant
Textbook and software