ABSTRACT
Bilinear systems evolve, as natural models or as accurate approximations to numerous dynamical processes in engineering, economics, biology, ecology, etc., and in other uses bilinear control may be implemented to improve controllability of an otherwise linear system. In this note some sufficient conditions for complete controllability of the following nonhomogeneous BLS are discussed. Based on the “visualization” of the qualitative behavior of BLS on the plane, the planar case was completely resolved. Verification of the conditions is a difficult problem in the case of several dimensions, though in a number of specific situations they were detailed for the homogeneous BLS. A new qualitative method to analyze the global complete controllability of nonhomogeneous BLS was proposed. This chapter introduces necessary preliminaries and discusses several sufficient conditions for global complete controllability.
