Document Type

Article

Publication Date

2012

DOI

10.1137/110852760

Publication Title

SIAM Journal on Control and Optimization

Volume

50

Issue

5

Pages

2786-2813

Abstract

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 convergence for the feedback connection, it is shown definitively that local convergence is preserved under feedback. This had been an open problem in the literature until recently.

Comments

© 2012 Society for Industrial and Applied Mathematics.

Posted with the permission of the publisher.

Original Publication Citation

Thitsa, M., & Gray, W. S. (2012). On the radius of convergence of interconnected analytic nonlinear input-output systems. SIAM Journal on Control and Optimization, 50(5), 2786-2813. doi:10.1137/110852760

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