Dewilde, Patrick (Delft Univ. of Tech.)

Hierarchical Semi-Separable Systems: The State Space Structure

Scheduled for presentation during the Mini-Symposium "New directions and problems in operator theory and system theory" (MoA12), Monday, July 24, 2006, 10:50−11:15, Room 104b

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 25, 2024

Abstract

In recent years, the theory of hierarchically semi-separable systems (HSS systems) has undergone major developments. In this paper we give an account of the underlying state space structure and show that some of the major properties derive directly from this structure. The class of HSS systems is closed under system inversion and spectral factorization in the strict sense, and in a somewhat looser sense also closed under other major system theoretical operations such as inner-outer factorization. Much of the classical theory of sequential semi-separable systems (SSS systems) carries over to the HSS case, the results presented may pave the way for new properties in the line of 'systems defined on a tree'.