Stabilization of a given set of equilibrium states of nonlinear systems

Abstract

The problem of multiprogram stabilization of the given set of equilibrium states in the class of nonlinear time invariant systems is studied. A method for designing multiprogram control based on the idea of interpolation is proposed. Hermite's interpolation polynomial makes it possible to design a controller that provides the prescribed time invariant modes of operation for the closed-loop system and ensures their asymptotic stability. A theorem on sufficient conditions for the existence of a multiprogram control is proved. The results are illustrated by a practical example.