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Construction of algebraic and difference equations with a prescribed solution space

Lazaros Moysis; Nicholas P. Karampetakis — 2017

International Journal of Applied Mathematics and Computer Science

This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ)β(k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ). This work deals with the inverse...

On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems

Antonis-Ioannis G. Vardulakis; Nicholas P. Karampetakis; Efstathios N. Antoniou; Evangelia Tictopoulou — 2009

International Journal of Applied Mathematics and Computer Science

We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an irreducible-at-infinity generalized 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 of irreducibility and minimality of generalized state space realizations of polynomial (transfer function) matrices is pointed out...

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