Algebraic approach to analysis of discrete-time polynomial systems

In this paper, we focus on the discrete-time polynomial systems and present the modified algorithms for testing observability and accessibility based on the methods by D. Nešić. Our method uses not only quantifier elimination but also Gröbner basis and real root counting techniques for decision problems needed in checking the properties and incorporates the strategy to improve efficiency in testing equivalence of ideals. Moreover, we show that invertibility of the systems can be checked by using Gröbner basis technique and hence backward accessibility and transitivity can be tested in the similar way in finite time step.