Characterizations of Integral Input-to-state Stability for Bilinear Systems in Infinite Dimensions
نویسندگان
چکیده
For bilinear infinite-dimensional dynamical systems, we show the equivalence between uniform global asymptotic stability and integral inputto-state stability. We provide two proofs of this fact. One applies to general systems over Banach spaces. The other is restricted to Hilbert spaces, but is more constructive and results in an explicit form of iISS Lyapunov functions.
منابع مشابه
Global converse Lyapunov theorems for infinite-dimensional systems
We show that existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided an additional mild assumption is fulfilled. For UGAS infinite-dimensional systems with external disturbances we derive a novel ’integral’ construction of non-coercive Lipschitz continuous Lyapunov functions. F...
متن کاملLocal input-to-state stability: Characterizations and counterexamples
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 p...
متن کاملConstrained Input-to-state Stability of Nonlinear Systems
Input-to-state stability (ISS), integral-ISS (iISS) and their related notions of input/output stability and detectability have become a useful framework for nonlinear feedback analysis and design. In this paper, a new notion, that of constrained input-to-state stability (cISS), is presented and several characterizations of cISS are obtained. cISS, unlike ISS or iISS, is not confined to forward ...
متن کاملA characterization of integral input-to-state stability
The notion of input-to-state stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite 2 gains. It plays a central role in recursive design, coprime factorizations, controllers for nonminimum phase systems, and many other areas. In this paper, a newer notion, that...
متن کاملIEEE TAC 1 A Characterization of Integral Input to StateStabilityDavid
| The notion of input to state stability (iss) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of nite gains with respect to supremum norms and also of nite L 2 gains. It plays a central role in recursive design, coprime factor-izations, controllers for non-minimum phase systems, and many other areas. In this paper, a newer notion, th...
متن کاملذخیره 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 2016