Time-varying nonlinear systems. Theorems on exponential and uniform asymptotic stability. Linear Time-varying systems and stronger stability conditions.  Total stability under non-vanishing perturbations. Uniform ultimate boundedness. 

Invariance-like Theorems: LaSalle Theorem, Barbalat Lemma, LaSalle-Yoshizawa Theorem and Anderson and Moore Theorem.  Recalls on Passivity. Uniform Complete Observability (UCO) and invariance of UCO under output injection. 

Model-Reference Adaptive Control (MRAC) of Scalar  Linear Systems: Direct and Indirect Methods. Asymptotic Stability of Adaptive Systems. Persistency-of-excitation conditions.

The Issue of Robustness. Robust Modifications of Passivity-based Update Laws. Update Laws with Leakage. Update Laws with Leakage and Dead-zone modification. Update Laws with Parameter Projection.

Model-Reference Adaptive Control. Design for Linear SISO Systems. Design of the Certainty-Equivalence Controller. Controller Parametrization. Adaptive Design. Adaptive Observers. Observers for Linear Systems. Adaptive observer form.

Examples of Practical Applications