Synthesis of variable gain controllers for a class of uncertain nonlinear systems via piecewise Lyapunov functions

This paper deals with a design problem of a variable gain controller for a class of uncertain nonlinear systems via piecewise Lyapunov functions. The variable gain controller is designed so as to reduce the effect of uncertainties and nonlinear perturbations. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show sufficient conditions for the existence of the proposed variable gain controller. Finally, numerical examples are presented.