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Interconnections Of Nonlinear Systems Driven By L₂-Itô Stochastic Processes, Luis A. Duffaut Espinosa

Electrical & Computer Engineering Theses & Dissertations

Fliess operators have been an object of study in connection with nonlinear systems acting on deterministic inputs since the early 1970's. They describe a broad class of nonlinear input-output maps using a type of functional series expansion, but in most applications, a system's inputs have noise components. In such circumstances, new mathematical machinery is needed to properly describe the input-output map via the Chen-Fliess algebraic formalism. In this dissertation, a class of L₂-Itô stochastic processes is introduced specifically for this purpose. Then, an extension of the Fliess operator theory is presented and sufficient conditions are given under which …