On the reachability of a class of continuous bilinear systems

Abstract

It is well known that using differential geometric methods, the reachability of nonlinear systems can be checked via Lie algebra. Normally, the resultant checking condition is state dependent and requires complicated recursive Lie bracket operations. In this paper, it is shown that for dyadic bilinear systems, the reachability property is actually state independent, and hence a global property of the system. Specifically, it is proved that the Lie algebra condition is equivalent to the rank conditions of two constant matrices. As examples, the reachability of two real‐world systems is examined through the new checking condition.