Fliess operators on Lp spaces: convergence and continuity
نویسندگان
چکیده
Fliess operators as input–output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory. In the classical analysis of these operators, certain growth conditions on the coe3cients in their series representations insure uniform and absolute convergence, provided every input is uniformly bounded by some 4xed upperbound. In some emerging applications, however, it is more natural to consider other classes of inputs. In this paper, Lp function spaces are considered. In particular, it is shown that the classic growth conditions also provide su3cient conditions for convergence and continuity when the admissible inputs are from a ball in Lp[t0; t0 + T ], where T is bounded and p¿ 1. In addition, stronger global growth conditions are given that apply even for the case where T is unbounded. When the coe3cients of a Fliess operator have a state space representation, it is shown that the state space model will always locally realize the corresponding input–output map on Lp[t0; t0 + T ] for su3ciently small T ¿ 0. If certain well-posedness conditions are satis4ed then the state space model will globally realized the input–output mapping for unbounded T when the coe3cients satisfy the global growth condition. c © 2002 Elsevier Science B.V. All rights reserved.
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عنوان ژورنال:
- Systems & Control Letters
دوره 46 شماره
صفحات -
تاریخ انتشار 2002