Journal ArticleDOI
Stability properties of functional difference equations
TLDR
In this paper, a subclass of general functional difference equations is derived which retain their stability under appropriate perturbations, and the results of Hale and Cruz are extended to include difference equations on the Banach space of p-th power integrable functions and essentially bounded functions.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1974-12-01. It has received 49 citations till now. The article focuses on the topics: Functional equation & Finite difference method.read more
Citations
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Journal ArticleDOI
On the zeros of exponential polynomials
TL;DR: In this article, the authors studied the dependence of Z (a, r) on a, r, where each aj is a nonzero real number and r is an n-vector, and gave information about the preservation of stability with respect to variations in the delays.
Book ChapterDOI
Effects of Small Delays on Stability and Control
TL;DR: In this article, the underlying mechanisms and the important role difference equations and almost periodic functions are playing in these results, as well as the role of almost periodic function in the sensitivity of partial differential equations to small time delays.
Journal ArticleDOI
The effect of small delays in the feedback loop on the stability of neutral systems
Hartmut Logemann,Stuart Townley +1 more
TL;DR: In this article, it is shown that closed-loop stability of a neutral system with unstable open-loop difference operator obtained by applying a derivative feedback scheme is extremely sensitive to arbitrarily small time delays in the feedback loop.
Journal ArticleDOI
Brief paper: Stability problem of systems with multiple delay channels
TL;DR: For systems with a large number of state variables with multiple low-dimensional delay elements, this formulation allows a drastic reduction of computational cost as compared to the traditional differential-difference equation formulation when the discretized Lyapunov-Krasovskii functional method is used.
Journal ArticleDOI
A Review of Some Subtleties of Practical Relevance for Time-Delay Systems of Neutral Type
TL;DR: In this article, the authors review some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice, including the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Journal ArticleDOI
Stability of functional differential equations of neutral type
Marianito A. Cruz,Jack K. Hale +1 more
TL;DR: In this paper, the authors give sufficient conditions for the stability and instability of solutions of a large class of equations (1.1) in terms of functions similar to those occurring in the application of the second method of Liapunov to ordinary and functional differential equations of retarded type.
Journal ArticleDOI
A class of Neutral Functional Differential Equations
TL;DR: In this paper, the existence, uniqueness, and continuation of solutions to the initial value problem for neutral functional differential equations are investigated, and an analysis is made of the dependence of the solutions on the initial conditions and parameters, resulting in the derivation of a continuous dependence theorem.