M atthias Kawski (Member) B rett Newman (Member) C John J. S^t i t s (Member) R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. Formal power series methods provide effective tools for nonlinear system analysis. For a broad range of analytic nonlinear systems, their input-output mapping can be described by a Fliess operator associated with a formal power series. In this dissertation, the inter connection of two Fliess operators is

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... haracterized by the generating series of the composite system. In addition, the formal Laplace-Borel transform of a Fliess operator is defined and its fundam ental properties are presented. The formal Laplace-Borel transform produces an elegant description of system interconnections in a purely algebraic context. Specifically, four basic interconnections of Fliess operators are addressed: the parallel, product, cascade and feedback connections. For each interconnection, the generating series of the overall system is given, and a growth condition is developed, which guarantees the convergence property of the output of the corresponding Fliess operator. M otivated by the relationship between operations on formal power series and system interconnections, and following the idea of the classical integral Laplace-Borel transform , a new formal Laplace-Borel transform of a Fliess operator is proposed. The properties of this Laplace-Borel transform are provided, and in particular, a fundam ental semigroup isomorphism is identified between the set of all locally convergent power series and the set of all well-defined Fliess operators. A software package was produced in Maple based on the ACE package developed by R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. Ill the ACE group in Universite de Marne-la-Vallee led by Sebastian Veigneau. The ACE package provided the binary operations of addition, concatenation and shuffle product on the free monoid of formal polynomials. In this dissertation, the operations of composition, modified composition, chronological products and the evaluation of Fliess operators are implemented in software. The package was used to dem onstrate various aspects of the new interconnection theory. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.