Blockwise estimate of the fundamental matrix of linear singularly perturbed differential systems with small delay and its application to uniform asymptotic solution
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TLDR
In this paper, a singularly perturbed system of linear differential equations with a small delay is considered, and estimates of blocks of the fundamental matrix solution to this system uniformly valid for all sufficiently small values of the parameter of singular perturbations are obtained in the cases of time independent and time dependent coefficients of the system.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2003-02-15 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Method of matched asymptotic expansions & Fundamental matrix (linear differential equation).read more
Citations
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A finite difference method for singularly perturbed differential-difference equations with layer and oscillatory behavior
TL;DR: In this article, a finite difference method for singularly perturbed linear second order differential-difference equations of convection-diffusion type with a small shift is presented, where the second order derivative is multiplied by a small parameter and the shift depends on the small parameter.
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On stabilization of nonstandard singularly perturbed systems with small delays in state and control
TL;DR: A composite feedback control exponentially stabilizing the original system is constructed based on stabilizing controls of the reduced-order and boundary-layer systems.
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On singularly perturbed small step size difference-differential nonlinear PDEs
TL;DR: In this article, a family of singularly perturbed small step size difference-differential nonlinear equations in the complex domain is studied and the authors construct formal solutions to these equations with respect to the perturbation parameter, which are asymptotic expansions with 1-Gevrey order of actual holomorphic solutions on some sectors in near the origin in.
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A Novel Approach to Exact Slow-Fast Decomposition of Linear Singularly Perturbed Systems with Small Delays
TL;DR: A novel (direct) approach to exact slow-fast decomposition of the spectrum of a singularly perturbed system with a single pointwise small delay is proposed and the stability of a multilink single-sink optical network is analyzed.
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Solving optimal control problems with control delays using direct transcription
TL;DR: A new technique for treating control delays when using a direct transcription approach is investigated in this paper.
References
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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.
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The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
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TL;DR: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977 and attempts to maintain the spirit of that book and have retained approximately one-third of the material intact.
Journal ArticleDOI
Differential Equations: Stability, Oscillations, Time Lags
H. A. Antosiewicz,A. Halanay +1 more
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