Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
I-Inverness for polynomial matrices of non-constant rank
Systems & Control Letters
Algebraic geometric aspects of feedback stabilization
SIAM Journal on Control and Optimization
Output feedback stabilizability and stabilization algorithms for 2D systems
Multidimensional Systems and Signal Processing
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This paper presents two computational criteria concerning the strongstabilizabilities of SISO (single-input single-output) n-D shift-invariantsystems. The first one is an alternative necessary and sufficient conditionfor an n-D system to be stabilizable by a stable complex controller, whichis an explicitly computable geometric equivalent to the topological onerecently derived by Shiva Shankar. The second one is a necessary andsufficient condition for the stabilizability by a stable real controller,which can be viewed as a generalization of the well-known Youla‘s parityinterlacing property for the 1-D case. Furthermore, related prolems forcomputational testing of the criteria are summarized and some basic ideas onpotential solution methods based on the cylindrical algebraic decompositionof algebraic varieties are outlined.