Controlled differential inclusions and stabilization of uncertain dynamical systems

Deterministic design of stabilizing feedback controls for a class of uncertain dynamical systems is considered. Adopting a problem formulation based on differential inclusions (encompassing all possible realizations of uncertainty), a class of generalized feedback controls is described (with practical analogues in the form of discontinuous feedbacks) which guarantees (a) global uniform asymptotic stability of the zero state and (b) ultimate attainment of prescribed model behaviour.