XU, LI (Akita Prefectural Univ.), Fan, Huijin (Huazhong Univ. of Science and Tech.), Lin, Zhiping (Nanyang Tech. Univ.), Bose, N. K. (The Pennsyvania State Univ.)

A Direct-Construction Approach to Multidimensional Realization and LFR Uncertainty Modeling

Scheduled for presentation during the Mini-Symposium "Multidimensional systems: Algebraic and behavioral approaches" (ThA11), Thursday, July 27, 2006, 11:40−12:05, Room 104a

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 May 19, 2024

Abstract

This paper proposes a direct-construction realization procedure which simultaneously treats all the involved variables and/or uncertain parameters and directly generates an overall Roesser model realization or LFR model for a given nD causal transfer matrix with rational function or polynomial entries. It is shown that the nD realization problem for an nD transfer matrix G(z_1,...,z_n), which is assumed without loss of generality to be strictly causal and given in the form of G=ND^{-1} with D(0,...,0)=I and N(0,...,0)=0, can be essentially reduced to the construction of an admssible nD polynomial matrix Psi for which there exist matrices A, B, C such that N=CZPsi and Psi D^{-1}=(I-AZ)^{-1}B with Z being the corresponding variable and/or uncertainty block structure. This important fact reveals a substantial difference between the 1D and nD (n>1) realization problems as in the 1D case Psi can only be a monomial matrix and never a polynomial one, and implies the possibility to achieve a realization with lower order than the constructive realization method given recently by the authors. Necessary and sufficient conditions that ensure Psi to be admissible are given and, based on these conditions, algorithms are proposed for construction of an admissible Psi with lower order and the corresponding realization. Illustrative examples are presented to illustrate the basic ideas and the effectiveness of the proposed method.