On the solution space of discrete time AR-representations over a finite time horizon (Q1826816)

The author studies the solution vector space of a discrete time nonregular AR-representation over a finite time nonregular AR-representation over a finite time interval which is divided into equivalence class, where each equivalence class represents the whole number of solutions of the AR-representation under certain boundary values. The dimension of the new equivalence class space is determined and is shown to be equal to the sum of the degrees of the finite and infinite elementary divisors plus two times the sum of the right minimal indices of the polynomial matrix that describes the AR-representation. An algorithm for the construction of the forward and backward solution space of a nonregular discrete time AR-representation over a finite time interval is given in terms of the structural invariants of the polynomial matrix which describe the system.