Hankel model reduction for descriptor systems

This paper focuses on model reduction of dynamical systems described by differential-algebraic equations. After transforming the system to the Weierstrass canonical form, the system is decomposed as a slow subsystem and a fast subsystem, which are then combined in parallel interconnection. Based on the solutions of these two subsystems, a new definition of the Hankel operator is given. Then, the conventional Hankel norm model reduction method is applied to the slow subsystem. Furthermore, we develop a new realization method to minimize the order of the fast subsystem while the DAE index is preserved. A numerical example is tested to show the approximation accuracy.