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Approximate and stable separable polynomial factorization. (English) Zbl 0861.93020
Multivariable polynomials play a crucial role in multivariable ($$n$$D) systems investigation. The complicated underlying ring structure is the source of numerous heavy problems in this theory. The situation is much more simpler when polynomials may be factorized into one variable factors. Unfortunately, this is not generally possible. From this point of view, approximate factorization, which is the subject of this paper, could be of significant interest. However, it seems that such approximation must be employed very carefully with some additional requirements. First of all, it must be clearly stated that stability of a system is not the effect of the procedure, but is preserved by it.

##### MSC:
 93C35 Multivariable systems, multidimensional control systems 12D05 Polynomials in real and complex fields: factorization