A Hankel matrix approach to singular system realization theory

A Hankel matrix approach to singular system realization theory is presented. The focus is exclusively on discrete-time or descriptor systems. Based on definitions of reachability and observability, the notion of a system Hankel matrix is first defined. The system Hankel matrix is then shown to have reachability-observability matrix factorizations which can be used to solve the realization synthesis problem. The notion of a balanced realization for singular systems is derived using the singular value decomposition of the system Hankel matrix. The theory is applied to synthesizing realizations which have minimum parametric sensitivity properties. It is demonstrated that such realizations are related to the notion of balancing.<>