Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this paper, the authors present the distributional theory of asymptotic expansions for functions of one variable, where the multidimensional expansions are studied in the central part of the book.
Abstract: The purpose of this chapter is to present the distributional theory of asymptotic expansions for functions of one variable. This chapter and the next, where the multidimensional expansions are studied, are the central part of the book.
48 citations
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TL;DR: In this article, a formal asymptotic solution of the Hamiltonian boundary-value problem with delay in the state variables is proposed and the justification of this solution is done.
Abstract: The Hamiltonian boundary-value problem, associated with a singularly-perturbed linear-quadratic optimal control problem with delay in the state variables, is considered. A formal asymptotic solution of this boundary-value problem is constructed by application of the boundary function method. The justification of this asymptotic solution is done. The asymptotic solution of the Hamiltonian boundary-value problem is constructed and justified assuming boundary-layer stabilizability and detectability.
48 citations
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18 Jun 199648 citations
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TL;DR: A technique is presented that uses numerical solutions to verify the order of the accuracy of an asymptotic expansion for several types of problems.
Abstract: A technique is presented that uses numerical solutions to verify the order of the accuracy of an asymptotic expansion for several types of problems. This technique may be introduced in any beginning course on asymptotic or perturbation methods, but is equally suited to verifying advanced asymptotic results.
47 citations
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TL;DR: In this paper, the authors investigate the local asymptotic stabilizability of a real analytic control system around an equilibrium point and give necessary and sufficient conditions for local stabilization using continuous feedback.
47 citations