On boundary implications of stability and positivity properties of multidimensional systems

Article Abstract:

The increasing need for study of digital filters and feedback systems described by more than one transform variable motivates study of the multidimensional extensions of the robustness of the stability property of polynomials and the positivity property of rational functions. A set of techniques that rely mainly on passive network theory are shown to generalize from 1-D to higher dimensions.

Mathematics of Computing, Scientific Research, Theory of Computation

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Sufficient Conditions for Stability of Multidimensional Discrete Systems

Article Abstract:

There are m additional sufficient conditions for the multidimensional part of a stability test of an n-dimensional filter or system. M+1 is the number of monomials in the denominator of the transfer function. The theorem and proof are given.

Stability, Mathematical Proofs, Filters, Transfer Functions, Applied Mathematics

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Comments on 'Sufficient conditions for existence and diffeomorphism of a nonlinear vector function.' (technical)

Article Abstract:

The theorems proposed by Prasad and Sharma for nonlinear vector functions are incorrect as stated. When the proof is worked through, the function x sine of x is surjective. A corrected version is presented.

Mathematical logic, Matrices (Mathematics), Nonlinear Algebra, Matrices, Functions, Functions (Mathematics)

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