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

by Dr. Takis Zourntos

  • 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