Construction of algebraic and difference equations with a prescribed solution space - Moysis, Lazaros; Karampetakis, Nicholas P. (Zielona Góra: Uniwersytet Zielonogórski)
This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(?) ? (k) = 0, where ? denotes the shift forward operator and A(?) 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(?) .
Keywords: algebraic and difference equations; behavior; exact modeling; auto-regressive representation; discrete time system; higher order system