Course Details

Course details of EE6415
Course NoEE6415
Course TitleNonlinear Systems Analysis
Course Content1. Mathematical preliminaries: Open and closed sets, compact set, dense set, Continuity of functions, Lipschitz condition, Vector space, norm of a vector, normed linear space, inner product space. 2. Examples of nonlinear systems drawn from mechanical, electrical, biological and chemical systems. Notion of equilibrium points and operating points, Jacobian linearization. 3. Second-order nonlinear systems , vector field, trajectories, flow, vector field plot, phase-plane portrait and positively invariant sets. Classification of equilibrium points based on the eigenvalues of the linearized system. Periodic solutions and the notion of limit cycles, Bendixson’s theorem and Poincare-Bendixson criteria. 4. Stability notions such as Lagrange, Lyapunov, asymptotic, global asymptotic, exponential, input-to-state (ISS) and instability. Lyapunov’s direct and indirect method, La Salle’s invariance principle and singular perturbations, set stability and stability of center manifold. Sum-of-Squares based construction of Lyapunov functions. 5. Design methods: Control laws based on Lyapunov function and Sliding mode control on benchmark examples.
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