On Some Approaches to Linearization of Affine Systems

Abstract

Abstract In this paper, we consider a problem of transforming a nonlinear control system into a linear controllable system. For affine control systems, we introduce the notion of A-orbital feedback equivalence which generalizes the concept of orbital feedback equivalence. We study the A-orbital feedback equivalence of a single-input affine control system with n state variables to a control system which can be considered as a linear controllable system with n — 1 state variables. For this case, we prove a necessary and sufficient condition for A-orbital feedback equivalence, develop an algorithm for transforming an affine system into a linear controllable system, and establish a relationship between A-orbital feedback equivalence and orbital feedback equivalence.