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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: A new equivalent sufficient condition is given for the neutral delay differential-algebraic equations to be delay-independent asymptotically stable and theAsymptotic stability of the numerical solutions generated by the Runge--Kutta methods combined with Lagrange interpolation is investigated.
Abstract: This paper is concerned with asymptotic stability of linear neutral delay differential-algebraic equations and Runge--Kutta methods. First, we give a new equivalent sufficient condition for the neutral delay differential-algebraic equations to be delay-independent asymptotically stable. Then we investigate the asymptotic stability of the numerical solutions generated by the Runge--Kutta methods combined with Lagrange interpolation. Some results on the asymptotic stability of Runge--Kutta methods of high order are given. Finally, numerical examples of index 1 and 2 are conducted to confirm our numerical stability result.

13 citations

Journal ArticleDOI
TL;DR: In this paper, the stability properties of the error dynamics are studied in the original coordinates and it is shown how the asymptotic stability in the new coordinates does not imply, in general, the original ones.
Abstract: Observer design for non-linear systems is discussed. Some recent approaches are based on state and output change of coordinates to transform a non-linear system into a particular observer form, from which an asymptotic observer can be designed ensuring the asymptotic stability of the error dynamics in the new coordinates. In this paper, the stability properties of the error dynamics are studied in the original coordinates. With some examples, it is shown how the asymptotic stability in the new coordinates does not imply, in general, the asymptotic stability in the original ones. Some general results are stated and proved to guarantee the asymptotic stability of the error dynamics in the original coordinates.

13 citations

Journal ArticleDOI
J. Yin1
TL;DR: In this article, asymptotic stability in probability and stabilization designs of discrete-time stochastic systems with state-dependent noise perturbations were investigated. And the convergence theorem of supermartingale was proved.
Abstract: Summary This paper investigates asymptotic stability in probability and stabilization designs of discrete-time stochastic systems with state-dependent noise perturbations. Our work begins with a lemma on a special discrete-time stochastic system for which almost all of its sample paths starting from a nonzero initial value will never reach the origin subsequently. This motivates us to deal with the asymptotic stability in probability of discrete-time stochastic systems. A stochastic Lyapunov theorem on asymptotic stability in probability is proved by means of the convergence theorem of supermartingale. An example is given to show the difference between asymptotic stability in probability and almost surely asymptotic stability. Based on the stochastic Lyapunov theorem, the problem of asymptotic stabilization for discrete-time stochastic control systems is considered. Some sufficient conditions are proposed and applied for constructing asymptotically stable feedback controllers. Copyright © 2014 John Wiley & Sons, Ltd.

13 citations

Journal ArticleDOI
TL;DR: In this paper, sufficient conditions for the uniform global asymptotic stability of the zero solution of (1.1) were given, and sufficient conditions were also given for the stability of (2.
Abstract: In this paper sufficient conditions for the uniform global asymptotic stability of the zero solution of (1.1) are given.

13 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of testing the hypothesis about the sub-mean vector and showed that the asymptotic expansion of the null distribution of Rao's U-statistic under a general condition is obtained up to order of n^-^1.

13 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526