连续时间系统的输入-状态稳定性有限时间李雅普诺夫函数

Q4 Mathematics

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2020-01-01 DOI:10.56082/annalsarscimath.2020.1-2.581

A. Doban, M. Lazar

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引用次数: 0

摘要

本文基于状态范数的正定函数的有限时间减小条件，提出了连续系统的输入-状态稳定性判据。这产生了所谓的ISS有限时间Lyapunov函数，与标准ISS Lyapunov函数相比，它允许更容易地选择候选函数。给出了利用有限时间李雅普诺夫函数的另一种逆ISS定理。此外，我们利用massera型构造证明了ISS有限时间Lyapunov函数与标准ISS Lyapunov函数是等价的。所开发的ISS框架可以与Sontag的“通用”稳定公式结合使用，分别为控制输入和干扰输入仿射的连续时间非线性系统开发输入到状态的稳定控制律。Msc: 93c10, 93d09, 93d30, 93d15

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INPUT-TO-STATE STABILITY FINITE-TIME LYAPUNOV FUNCTIONS FOR CONTINUOUS-TIME SYSTEMS

In this paper we propose an input-to-state stability (ISS) criterion for continuous–time systems based on a finite–time decrease condition for a positive definite function of the norm of the state. This yields a so–called ISS finite–time Lyapunov function, which allows for easier choice of candidate functions compared to standard ISS Lyapunov functions. An alternative converse ISS theorem in terms of ISS finite– time Lyapunov functions is also provided. Moreover, we prove that ISS finite–time Lyapunov functions are equivalent with standard ISS Lyapunov functions using a Massera–type construction. The developed ISS framework can be utilized in combination with Sontag’s “universal” stabilisation formula to develop input–to–state stabilizing control laws for continuous–time nonlinear systems that are affine in the control and disturbance inputs, respectively. MSC: 93C10, 93D09, 93D30, 93D15

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.