Conditions for strong stabilizabilities of n-dimensional systems

This paper presents two computational criteria concerning the strong stabilizabilities of SISO (single-input single-output) n-D shift-invariant systems. The first one is an alternative necessary and sufficient condition for an n-D system to be stabilizable by a stable complex controller, which is an explicitly computable geometric equivalent to the topological one recently derived by Shiva Shankar. The second one is a necessary and sufficient condition for the stabilizability by a stable real controller, which can be viewed as a generalization of the well-known Youla's parity interlacing property for the 1-D case. Furthermore, related prolems for computational testing of the criteria are summarized and some basic ideas on potential solution methods based on the cylindrical algebraic decomposition of algebraic varieties are outlined.