On some triangular structures and the state dead-beat problem for polynomial systems

The quantifier elimination by partial cylindrical algebraic decomposition (QEPCAD) based controllability testing for polynomial discrete-time systems is computationally very expensive and it may lead to non-terminating algorithms. We identify the structure of a large class of polynomial discrete-time systems, which reduces the computational cost associated with the dead-beat controllability test and which may lead to finite time controllability tests. For this purpose we use QEPCAD and the Grobner basis method. The structure which we identify encompasses several classes of systems for which dead-beat controllability tests exist.