Local input-to-state stability: Characterizations and counterexamples
نویسنده
چکیده
We show that a nonlinear locally uniformly asymptotically stable infinite-dimensional system is automatically locally input-to-state stable (LISS) provided the nonlinearity possesses some sort of uniform continuity with respect to external inputs. Also we prove that LISS is equivalent to existence of a LISS Lyapunov function. We show by means of a counterexample that if this uniformity is not present, then the equivalence of local asymptotic stability and local ISS does not hold anymore. Using a modification of this counterexample we show that in infinite dimensions a uniformly globally asymptotically stable at zero, globally stable and locally ISS system possessing an asymptotic gain property does not have to be ISS (in contrast to finite dimensional case). © 2015 Published by Elsevier B.V.
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ورودعنوان ژورنال:
- Systems & Control Letters
دوره 87 شماره
صفحات -
تاریخ انتشار 2016