A Piecewise Smooth Control-Lyapunov Function Framework for Switching Stabilization
Abstract
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.
Cite
@article{arxiv.1503.01968,
title = {A Piecewise Smooth Control-Lyapunov Function Framework for Switching Stabilization},
author = {Yueyun Lu and Wei Zhang},
journal= {arXiv preprint arXiv:1503.01968},
year = {2015}
}