Topology and asymptotic controllability of switched control systems

Date

2003-12

Journal Title

Journal ISSN

Volume Title

Publisher

Texas Tech University

Abstract

A fundamental requirement for the design of feedback control systems is the knowledge of the structural properties of the plant under consideration. These properties are closely related to the concepts of controllability, stability and stabilizability. One major issue regarding switched control systems is to control them while maintaining their stabilizability. Control design for switched control systems is known to be a nontrivial problem. Here, an indirect approach is taken to resolve the switched control design problem; it is shown that trajectories of controllable switched systems consisting of linear continuous-time time-invariant subsystems can be approximated arbitrarily closely by those of related controllable time-invariant non-switched polynomial systems. Examples are obtained to demonstrate the fact that the class of controllable switched systems consisting of linear continuous-time time-invariant subsystems are not locally asymptotically stabilizable via continuous switching strategies in general. Asymptotic feedback controllability of the aforementioned class of switched control systems is then established.

Finally, it is proved that the controllable switched systems consisting of linear continuous-time time-invariant subsystems have a GL{n, R) x Sk-principal fiber-bundle structure. Manifold structure of certain subclasses of it is made explicit, by deriving canonical forms for the base manifold. These structures are used to derive explicit formulas for control inputs in order to achieve asymptotic controllability to the origin.

Description

Keywords

Feedback control systems -- Design and construction, Switching theory, Linear -- Asymptotic theory, Differential equations, Feedback control systems -- Mathematical models

Citation