Dynamic Feedback Equivalence of Nonlinear Systems on Time Scales

Authors:	Bartosiewicz Zbigniew, Bialystok Technical University, Poland Pawluszewicz Ewa, Bialystok Technical University, Poland
Topic:	2.3 Non-Linear Control Systems
Session:	Feedback Linearization
Keywords:	Behaviour; control system; differential equations; continuous-timesystems; discrete-time systems; dynamic feedback; feedbacklinearization; nonlinear control systems

Abstract

The problem of dynamic feedback equivalence of nonlinear control systems on time scales is studied. Time scale is a model of time. Two most important cases are the real line (continuous time) and the set of integers (discrete time). Control systems on time scales include continuous-time and discrete-time systems. The delta algebra of a nonlinear control system is introduced. The main result says that two systems defined on a time scale are dynamically feedback equivalent if and only if their delta algebras are isomorphic. This is an extension of continuous-time and discrete-time versions.