Realization and Structure Theory of Bilinear Dynamical Systems

Starting from the description of the system provided by the series expansion of the zero-state response, this paper develops the realization theory for bilinear systems. It is shown that the condition of realizability corresponds to that of the factorizability of the kernels of this expansion. The paper then analyzes the properties of the minimal and nonminimal factorizations and provides a solution of the problem of characterizing the minimal realizations. Subsequently, developing the structure analysis of the state space, it is shown that there exists a canonical form of the equations and the results of the realization theory are interpreted on this basis. Lastly, the bases are laid for developing realization procedures, and it is shown that the sequence of kernels of a bilinear system is completely identified by a finite number of these kernels.