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On continued fractions for modelling and simulation of systems. (English) Zbl 0749.40003

The author shows that the algorithms for determining continued fraction expansions (CFEs) of a system can be directly obtained from positive and/or negative power series expansion. The algorithms establish direct link between CFE and state space representation and can therefore be used for modelling and simulation of systems described by irrational functions without requiring to determine the rational function approximation. Algorithm for determining CFE and continued fraction inversion can be used to determine the transfer function from a given state space model. He has also derived expressions for the numerator and denominator polynomials of rational functions corresponding to the CFEs considered by him. In order to have approximate state space representation of systems described by irrational functions, two canonical forms based on continued fractions have been considered by him and some results regarding these continued fractions have been derived.

MSC:

40A15 Convergence and divergence of continued fractions
30B70 Continued fractions; complex-analytic aspects
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
65D15 Algorithms for approximation of functions
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