The Multiplicity of Eigenvalues of a Vectorial Sturm-liouville Problem

Abstract

In this paper, we consider the approximate stabilization of a class of switched nonlinear system composed of a finite family of subsystems. We show that there exists a piecewise constant feedback controller such that the system can achieve the approximate stabilization property under arbitrary switching signal. We also discuss the numerical computation problem in determining the control input value at the sampling instant or switching instant and present a method to solve the problem.