Input Independent Stability of a Bilinear System

Abstract

This paper deals with a stability problem of a bilinear system described by x=Ax+Bxu, which arises in the study of an observer and controllability of bilinear systems. The condition under which the system is asymptotically stable in the large independent of the input u is discussed. A necessary condition and a sufficient condition in terms of matrices A and B are derived. And it is shown that this sufficient condition is also necessary for a single-input two-dimensional system to be stable. Another sufficient condition, which can be easily verified, is given for the single-input system.