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The exhaustive list of topics in Nonlinear Control System in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Mathematical preliminaries on point-set topology, normed spaces, Lipschitz continuity, existence and uniqueness of solution of ODE's.
  • Modelling of simple mechanical systems, degree-of-freedom, configuration spaces and state-space representation, equilibrium points/operating points, Jacobian linearization.
  • Notion of vector field, trajectories, vector field plot, phase-plane portrait, positively invariant sets and classification of equilibrium points.
  • Second-order systems, Periodic solution, Bendixson's theorem and Poincare-Bendixson criteria.
  • Various notions of stability such as Lyapunov stability, Asymptotic stability, Exponential stability.
  • Stabilty analysis using Lyapunov's direct and indirect method, La Salles's invariance principle and singular perturbation.