Abstract
This paper presents a constructive approach to the problem of output feedback stabilizability and stabilization of a class of linear multidimensional (nD, n>2) systems, whose varieties of the ideals generated by the reduced minors are infinite with respect to not more than two variables. The main idea of the proposed approach is to decompose the variety of an nD system in this class into a union of several varieties, each of which is defined by polynomials in just two variables. The new method can be considered as a combination of Gröbner bases and existing results on two-dimensional (2D) digital filter stability tests and on stabilizability and stabilization of 2D systems. An example is illustrated.
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Lin, Z., Lam, J., Galkowski, K. et al. A Constructive Approach to Stabilizability and Stabilization of a Class of nD Systems. Multidimensional Systems and Signal Processing 12, 329–343 (2001). https://doi.org/10.1023/A:1011909707499
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DOI: https://doi.org/10.1023/A:1011909707499