On gramians and balanced truncation of discrete-time bilinear systems

This paper obtains a balanced truncation model reduction method for discrete-time bilinear systems. After deriving the sufficient conditions for the discrete-time bilinear systems to lead to bounded outputs for some bounded inputs, we study the properties of the reachability and observability gramians. The gramians can be computed by solving two generalized Lyapunov equations. By balancing the reachability and observability gramians, a model reduction method is obtained. Some propositions of the reduced order models are given. A numerical example is given to illustrate the effectiveness of the proposed method.