State feedback stabilization of a class of discontinuous systems

This paper investigates the feedback stabilization problems for a class of discontinuous nonlinear systems. A set-valued time derivative is introduced for nonsmooth function along discontinuous vector fields, which enables us to perform Lyapunov-based design with non-regular Lyapunov function for the Fillipov solutions. The first result is to give a design approach to a discontinuous feedback control law for a class of nonlinear systems under a matched discontinuity. Then, it is shown that the control law, as virtual control, can be extended to recursive design problem when the control input is provided by an integrator. Numerical example is given to illustrate the design approach.