The main aim is to introduce the concepts and theoretical techniques needed to study the stability and stabilization of nonlinear control systems, with particular attention being paid to Lyapunov-based analysis and design of control feedback laws.

The students will be able to study systems using techniques based on the following:
-Phase-plane analysis: understanding how solutions can evolve in state-space for bidimensional systems
-Lyapunov functions, invariant sets and Lasalle's theory: assessing stability of equilibria on the basis of monotonicity properties of suitably selected energy-like functions
-Input-to-State Stability: assessing robustness of a nonlinear control system subject to exogenous disturbances
- the Small-Gain Theorem and passivity: testing stability for systems connected in cascade or in feedback

For non-linear systems, methods for determining stability and for designing stabilising controllers are studied using state-space methods (Lyapunov theory, backstepping, feedback linearization) and input-output approaches (small gain theorem, passivity, input-to-state stability).