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On a class of PDEs with nonlinear distributed in space and time state-dependent delay terms

✍ Scribed by Alexander V. Rezounenko

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
157 KB
Volume
31
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

A new class of nonlinear partial differential equations with distributed in space and time state‐dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state‐dependent delay and discuss advantages of this class. Local and long‐time asymptotic properties, including the existence of global attractor and a principle of linearized stability, are studied. Copyright © 2008 John Wiley & Sons, Ltd.

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## Abstract In this paper, the problem of robust passive control for a class of nonlinear systems with time‐varying delays is considered. The uncertainties investigated in this paper are norm bounded and time varying, and they enter all system matrices. Based on the Lyapunov–Krasovskii functionals