Nonlinear Systems    

School of ECE, University of Tehran

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  Course Outline

          ● Introduction to Nonlinear Systems

          ● Nonlinear State Models

          ● Properties of Solutions of ODEs

          ● Phase Plane Analysis

          ● Limit Cycles

          ● Lyapunov Theory for Autonomous Non-autonomous Systems

          ● The Invariance Principle and LaSalle's Theorem

          ● Barbalat's Lemma

          ● Domain of Attraction and It's Estimation 

          ● Bifurcation

          ● The Center Manifold Theorem

          ● Boundedness and Ultimate Boundedness

          ● Stability of Perturbed Systems: Vanishing and Non-Vanishing Perturbations

          ● Slowly varying systems

          ● Singular Perturbations

          ● Passivity and Dissipativity

          ● Absolute Stability: Circle and Popov Criteria

          ● Input-to-State Stability

          ● Input-to-Output Stability

          ● Small-Gain Theorem

          ● Final Projects: New Applied/Theoretical Emerging Topics

    

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