Special Topics in Nonlinear Dynamical Systems: Lyapunov Methods (ECEN 689)

Introduction to nonlinear systems
     – Mathematical preliminaries
     – Difference betwen linear and nonlinear response
     – Qualitative behavior of linear systems: phase portraits
     – Nonlinear systems’ phase portraits: multiple equilibria, limit cycles, finite escape time, local stability

Fundamental properties
     – Existence and uniqueness
     – Locally Lipschitz and globally Lipschitz nonlinearities
     – Boundedness: Comparison principle

Lyapunov stability
     – Lyapunov stability for autonomous systems, LaSalle invariance principle
     – Lyapunov stability for non-autonomous systems: Barbalat's lemma
     – Converse theorems
     – Asymptotic stability, uniform stability, global asymptotic stability, exponential stability

Nonlinear control techniques
     – Gain scheduling
     – Lyapunov redesign
     – Backstepping
     – Sliding mode control