Classifications of Generalized Linear Control Systems

Abstract

We concern with the classification problem of generalized linear control systems, which might be useful for some engineering applications. Inspired by the work of Shayman and Zhou in 1987, we give the definition of linear, differentiable and topological equivalence for a special class of generalized linear systems in a unified way. Then we derive some properties on these three kinds of equivalences and show the canonical forms through a concrete example. In this paper, we obtain natural generalizationsof the Brunovsky's feedback equivalence theorem and the Willems' topological classification theorem for usual linear control systems.