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.