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Approximate stable multidimensional polynomial factorization into linear \(m\)-D polynomial factors. (English) Zbl 0880.93022
This paper is one of a considerable number of publications written by the author devoted to approximate factorisation of multidimensional polynomials. This problem may be very interesting and significant for \(nD\) systems investigations due to the fact that, as the author mentions too, the analysis of systems with separable characteristic polynomials is considerably simpler. The point is, however, how to guarantee that some features such as stability are invariant under the factorisation procedure. This problem seems to be very difficult. It seems that using the factorisation procedure as the tool for improving polynomials, i.e. synthesizing a stable polynomial from an unstable one, which is suggested by the author here, is complete nonsense. We mean the following: we have an active system (e.g. generator) and we approximate its mathematical model in such a way as, to obtain a passive system. This is possible but the approximated model does not have any relation to reality.
93C35 Multivariable systems, multidimensional control systems
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