EE 8215 – Nonlinear SystemsMihailo Jovanovic,
University of Minnesota, Spring 2016
Course descriptionIntroduction. Examples of nonlinear systems. Statespace models. Equilibrium points. Linearization. Range of nonlinear phenomena: finite escape time, multiple isolated equilibria, limit cycles, chaos. Bifurcations. Phase portraits. Bendixson and PoincareBendixson criteria. Mathematical background: existence and uniqueness of solutions, continuous dependence on initial conditions and parameters, normed linear spaces, comparison principle, BellmanGronwall Lemma. Lyapunov stability. Lyapunov's direct method. Lyapunov functions. LaSalle's invariance principle. Estimating region of attraction. Center manifold theory. Stability of timevarying systems. Inputoutput and inputtostate stability. Small gain theorem. Passivity. Circle and Popov criteria for absolute stability. Perturbation theory and averaging. Singular perturbations. Feedback and inputoutput linearization. Zero dynamics. Backstepping design. Control Lyapunov functions. Class schedule
TuTh, 2:30pm  3:45pm, Keller Hall 3115 Instructor and Teaching Assistant
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