Accessibility Lie algebra of switched bilinear systems

This paper considers the accessibility Lie algebra of switched bilinear systems (SBLS). First, its structure is investigated, which leads to an easily computable verification algorithm. Then its applications to the controllability of SBLS are presented.

I. Introduction

Accessibility Lie algebra plays a fundamental role in the investigation of controllability of nonlinear systems [7]. Frobenius’ Theorem and Chow's Theorem are the bridge to connect the accessibility Lie algebra with variety of controllabilities of nonlinear systems. We refer to [11] for Frobenius’ Theorem and to [1] for Chow's Theorem because they provide generalized versions for analytic case, which is suitable for bilinear systems.