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On The Radius Of Convergence Of Interconnected Analytic Nonlinear Input-Output Systems, Makhin Thitsa, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

A complete analysis is presented of the radii of convergence of the parallel, product, cascade and feedback interconnections of analytic nonlinear input-output systems represented as Fliess operators. Such operators are described by convergent functional series, which are indexed by words over a noncommutative alphabet. Their generating series are therefore specified in terms of noncommutative formal power series. Given growth conditions for the coefficients of the generating series for the subsystems, the radius of convergence of each interconnected system is computed assuming the subsystems are either all locally convergent or all globally convergent. In the process of deriving the radius of …