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The main purpose of this work is to determine the forward and backward solution space of a nonregular discrete time AR-representation i.e. A(σ)ξ(k) = 0, in a finite time horizon where A(σ) is a polynomial matrix and σ is the forward shift operator. The construction of the behavior is based on the structural invariants of the polynomial matrix that describes… (More)

The main purpose of this work is to determine the dimension of the solution space of a nonregular discrete time AR-representation i.e. A(σ)ξ(k) = 0, in a closed interval [0, N ] where A(σ) is a nonregular polynomial matrix and σ is the forward shift operator. It is shown that the dimension of the solution space of such a system is strongly related to the… (More)

The main purpose of this work is to propose new notions of equivalence between polynomial matrices, that preserve both the finite and infinite elementary divisor structure. The approach we use is twofold : a) the ”homogeneous polynomial matrix approach” where in place of the polynomial matrices, we study their homogeneous polynomial matrix forms and use 2-D… (More)

The main purpose of this work is to construct the forward and backward solution space of a nonregular discrete time AR-representation i.e. A(σ)ξ(k) = 0, in a closed interval [0, N ] where A(σ) is a polynomial matrix and σ is the forward shift operator. The construction of the behavior is based on the structural invariants of the polynomial matrix which… (More)

The aim of this work is twofold : a) it uses the fundamental matrix of the resolvent of a regular pencil in order to provide an algorithm for the computation of the fundamental matrix of the resolvent of a polynomial matrix, and b) it proposes a closed formula for the forward, backward and symmetric solution of an AutoRegressive Moving Average (ARMA). This… (More)

This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents… (More)

- Nikos P. Karampetakis
- 2006 IEEE Conference on Computer Aided Control…
- 2006

A new family of companion forms for polynomials and polynomial matrices has recently been developed in [4] and [1] respectively. The application of these new companion forms to polynomial matrices with symmetries has been examined in [2]. In this work we extend the results presented in [2] to the case of 2-D polynomial matrices and thus provide a new… (More)

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