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Full-Text Articles in Mathematics
Formal Power Series Approach To Nonlinear Systems With Static Output Feedback, G.S. Venkatesh, W. Steven Gray
Formal Power Series Approach To Nonlinear Systems With Static Output Feedback, G.S. Venkatesh, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and static output feedback is applied. The first step is to reconsider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback Hopf algebra used to describe dynamic output …
The Formal Laplace-Borel Transform Of Fliess Operators And The Composition Product, Yaqin Li, W. Steven Gray
The Formal Laplace-Borel Transform Of Fliess Operators And The Composition Product, Yaqin Li, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation …