Cyclic Vectors of Associative Matrix Algebras and Reachability Criteria for Linear and Nonlinear Control Systems

TL;DR

This paper investigates the existence of cyclic vectors in associative matrix algebras to derive controllability criteria for both linear and nonlinear control systems, addressing problems in switched systems and mechanical systems.

Contribution

It offers a new sufficient criterion for the existence of cyclic vectors, linking algebraic properties to controllability in control systems.

Findings

Provided a sufficient criterion for cyclic vector existence.

Connected algebraic conditions to controllability of control systems.

Applied results to both linear and nonlinear systems.

Abstract

Motivated by the controllability/reachability problems for switched linear control systems and some classes of nonlinear (mechanical) control systems we address a related problem of existence of a cyclic vector for an associative (matrix) algebra. We provide a sufficient criterion for existence of cyclic vector and draw conclusions for controllability.