Date of Award

Winter 2009

Document Type


Degree Name

Doctor of Philosophy (PhD)


Electrical & Computer Engineering


Electrical Engineering

Committee Director

W. Steven Gray

Committee Member

N. Rao Chaganty

Committee Member

Oscar R. Gonzalez

Committee Member

Dimitrie C. Popescu


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 these operators are convergent in the mean-square sense. Next, three types of system interconnections are considered in this context: the parallel, product and cascade connections. This is done by first introducing the notion of a formal Fliess operator driven by a formal stochastic process. Then the generating series induced by each interconnection is derived. Finally, sufficient conditions are given under which the generating series of each composite system is convergent. This allows one to determine when an interconnection of Fliess operators driven by a class of L2-Itô stochastic processes is well-defined.