Abstract
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.
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Ying, J.Q. Conditions for Strong Stabilizabilities of n-Dimensional Systems. Multidimensional Systems and Signal Processing 9, 125–148 (1998). https://doi.org/10.1023/A:1008226120181
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DOI: https://doi.org/10.1023/A:1008226120181