On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems

Author:

Vardulakis Antonis-Ioannis,Karampetakis Nicholas,Antoniou Efstathios,Tictopoulou Evangelia

Abstract

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space SystemsWe review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of anirreducible-at-infinitygeneralized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts ofirreducibilityandminimalityof generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts ofdynamicandnon-dynamicvariables appearing in generalized state space realizations are also examined.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference18 articles.

1. Realizations in generalized state-space form for polynomial system matrices and the definitions of poles, zeros and decoupling zeros at infinity;O. Bosgra;International Journal of Control,1981

2. Canonical forms for singular systems;M. Christodoulou,1986

3. Controllability, observability, and duality in singular systems;D. Cobb;IEEE Transactions on Automatic Control,1984

4. Generalized state space realizations of non-proper rational transfer functions;G. Conte;Systems and Control Letters,1982

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