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1 TTK4150 Nonlinear Control Systems Lecture 5 Stability analysis for autonomous systems Direct Lyapunov method continued Invariance principle 2 Previous lectures: stability of autonomous systems ã Stability of equilibrium points (autonomous systems) – Definitions (stability, asymptotic/exponential stability, global asymptotic/exponential stability, region of attraction) – Stability analysis using phase plane analysis – Stability analysis using indirect (linearization) Lyapunov method ã Stabilit
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  1 TTK4150 Nonlinear Control Systems Lecture 5 Stability analysis for autonomous systemsDirect Lyapunov method continuedInvariance principle  2 Previous lectures:stability of autonomous systems ãStability of equilibrium points (autonomous systems) –Definitions (stability, asymptotic/exponential stability, globalasymptotic/exponential stability, region of attraction) –Stability analysis using phase plane analysis –Stability analysis using indirect (linearization) Lyapunov methodãStability analysis using energy functionsãDirect Lyapunov method for stability analysis –Theorems for stability, asymptotic stability, global asymptotic stability, exponentialstability, global exponential stability –Application examples –Lyapunov functions: quadratic Lyapunov functions, examples, tricks  3 Today: ãDirect Lyapunov method for stability analysis –Lyapunov functions: examples, tricks, continued…ãInvariance principle –Definitions: compact sets, invariant sets, convergence to sets –Invariance principle + corollaries –Application exampleãEstimation of the region of attraction –Definition, examples –An algorithm  4 Literature ãKhalil Chapter 4 (Lyapunov functions tricks and examples) Chapter 4, Section 4.2, (Invariance principle) Chapter 8, Secton 8.2 (estimation of the region of attraction)
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