On the radius of convergence of interconnected analytic nonlinear systems.

摘要

A complete analysis is presented of the radii of convergence of the parallel, product, cascade and unity feedback interconnections of analytic nonlinear input-output systems represented as Fliess operators. Such operators are described by convergent functional series, indexed by words over a noncommutative alphabet. Their generating series are therefore specified in terms of noncommutative formal power series. Given growth conditions on the coefficients of the generating series for the component systems, the radius of convergence of each interconnected system is computed assuming the component systems are either all locally convergent or all globally convergent. In the process of deriving the radius of convergence for the unity feedback connection, it is shown definitively that local convergence is preserved under unity feedback. This had been an open question in the literature.