Generating Series and Nonlinear Systems: Analytic Aspects, Local Realizability, and I/o Representations

نویسندگان

  • Yuan Wang
  • Eduardo D. Sontag
چکیده

This paper studies fundamental analytic properties of generating series for nonlinear control systems, and of the operators they deene. It then applies the results obtained to the extension of facts, which relate realizability and algebraic input/output equations, to local realizability and analytic equations.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Analytic Constraints and Realizability for Analytic Input/Output Operators∗

For input/ouput (i/o) operators, an equivalence is shown between realizability by state space systems and the existence of analytic constraints on higher order derivatives of i/o signals. This provides a precise characterization of realizability, extending to the general analytic case previous work that dealt with the equivalence between algebraic realizability and algebraic i/o equations.

متن کامل

Generalized Input/Output Equations and Nonlinear Realizability∗

This work studies various types of input/output representations for analytic input/output operators. It is shown that if an operator satisfies an integro-differential input/output equation or an integral one, then it is locally realizable by analytic state space systems. This generalizes the results previously obtained for differential input/output equations to integral and integro-differential...

متن کامل

On Generating Series and Convergence of Interconnected Analytic Nonlinear Systems

Most complex systems encountered in applications can be viewed in terms of interconnections of more elementary subsystems. A natural class of nonlinear systems to consider in this context is the set of analytic input-output systems known as Fliess operators. Such operators are described by convergent functional series which are indexed by words over a noncommutative alphabet. Their generating s...

متن کامل

A Faà di Bruno Hopf algebra for a group of Fliess operators with applications to feedback

A Faà di Bruno type Hopf algebra is developed for a group of integral operators known as Fliess operators, where operator composition is the group product. The result is applied to analytic nonlinear feedback systems to produce an explicit formula for the feedback product, that is, the generating series for the Fliess operator representation of the closed-loop system written in terms of the gen...

متن کامل

Globally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change‎, ‎I‎ : ‎Iwasawa algebras and a base change map

This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2‎, ‎mathbb{Z}_p)$‎. ‎It then describes a natural base change map between the Iwasawa algebras or more correctly‎, ‎as it turns out‎, ‎between the global distribut...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1991