  This paper studies switching stabilization problems for general switched
nonlinear systems. A piecewise smooth control-Lyapunov function (PSCLF)
approach is proposed and a constructive way to design a stabilizing switching
law is developed. The switching law is constructed via the directional
derivatives of the PSCLF with a careful discussion on various technical issues
that may occur on the nonsmooth surfaces. Sufficient conditions are derived to
ensure stability of the closed-loop Filippov solutions including possible
sliding motions. The proposed PSCLF approach contains many existing results as
special cases and provides a unified framework to study nonlinear switching
stabilization problems with a systematic consideration of sliding motions.
Applications of the framework to switched linear systems with quadratic and
piecewise quadratic control-Lyapunov functions are discussed and results
stronger than the existing methods in the literature are obtained. Application
to stabilization of switched nonlinear systems is illustrated through an
numerical example.
