Model Reduction of Bilinear Control Systems

In this paper, the problem of model reduction for discrete bilinear control systems is considered. Based upon the fundamental relationships among the system reachability, observability and stability, two methods for obtaining the reduced-order models are introduced. The first method applies the singular value decomposition on the generalized Hankel matrix which is defined in terms of the impulse response data. The second method utilizes the factorization of the reachability and observability Gramians. These Gramians are shown to satisfy generalized Lyapunov matrix equations under certain condtions. The order-reduction algorithms developed for bilinear systems have been tested on a fifth-order neutron kinetic model. A third-order model which is balanced with respect to both reachability and observability is shown to accurately approximate the original fifth-order model.