论文信息 - Truncated bilinear approximants: Carleman, finite volterra, Padé-type, geometric and structural automata

Truncated bilinear approximants: Carleman, finite volterra, Padé-type, geometric and structural automata

In this paper, two original infinite ℝ-automata representations of an analytic systems are provided, allowing to compute easily a large class of bilinear approximants, including the so called “Carleman linearization method” as well as the “finite Volterra expansions” and “Pade-type”.

C. Hespel | C. Hespel

[1] Marcel Paul Schützenberger,et al. On the Definition of a Family of Automata , 1961, Inf. Control..

[2] Pierre Leroux,et al. A Combinatorial Approach to Nonlinear Functional Expansions: An Introduction with an Example , 1991, Theor. Comput. Sci..

[3] Françoise Lamnabhi-Lagarrigue,et al. Algebraic Computing in Control , 1991 .

[4] M. Fliess,et al. Fonctionnelles causales non linaires et indtermines non commutatives , 1981 .

[5] Christiane Hespel,et al. Approximation of Nonlinear Dynamic Systems by Rational Series , 1991, Theor. Comput. Sci..

[6] Françoise Lamnabhi-Lagarrigue,et al. An algebraic approach to nonlinear functional expansions , 1983 .

[7] Philippe Flajolet. Combinatorial aspects of continued fractions , 1980, Discret. Math..

[8] T. Carleman. Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires , 1932 .

[9] C. Brezinski. Padé-type approximation and general orthogonal polynomials , 1980 .

[10] Roger W. Brockett. Volterra series and geometric control theory , 1976, Autom..