A computer algebra method for testing structural distinguishability of state space models

In practice we often have several model structures-candidates to describe the same phenomenon. In that case the task of selecting the best model structure (discrimination between the models) arises. But if the model structures are indistinguishable by input-output behavior, any attempt of discriminating between them is meaningless. Investigation of structural properties of state space models requires complicated algebraic manipulations with use of computer algebra methods. In present paper we derive conditions for structural distinguishability of state space model structures. On the basis of this condition we develop an effective method combining a Gaussian elimination method to form a system of equalities and inequalities with Buchberger algorithm for evaluation of Grobner basis to test if the generated system is compatible. The method is implemented in the computer algebra package MAPLE.