Continuity Properties of Nonlinear Affine Control Systems: Applications to Hybrid and Sliding Mode Dynamics

This paper focuses on the continuity and approximability properties for nonlinear affine control systems. We consider dynamical systems governed by ordinary differential equations and establish the continuity properties of the given and relaxed (in the sense of Filippov) systems with respect to controls and initial state variables. The approach based on the set-valued analysis makes it possible to study discontinuous models in the abstract setting and to obtain general theoretical results. The latter can be effectively applied to wide classes of variable structure control systems. In particular, this paper deals with applications of the above-mentioned continuity and approximability to some hybrid control systems and to the classical sliding mode control processes.