Input-to-state stability of non-autonomous infinite-dimensional control systems

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI:10.3934/mcrf.2022035

H. Damak

引用次数: 3

Abstract

This paper addresses input-to-state stability (ISS) and integral input-to-state stability (iISS) for non-autonomous infinite-dimensional control systems. With the notion of uniformly exponential stability scalar function, ISS and iISS are considered based on indefinite Lyapunov functions. In addition, we obtain several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities. As a result, the iISS criteria of non-autonomous bilinear systems is also established. Furthermore, an illustrative example is given to show the applicability of the results.

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非自治无限维控制系统的输入-状态稳定性

本文研究了非自治无限维控制系统的输入-状态稳定性和积分输入-状态稳定性。利用一致指数稳定标量函数的概念，在不定Lyapunov函数的基础上考虑了ISS和iISS。此外，我们还得到了用耗散不等式表示的iISS性质的几个必要和充分的表征。建立了非自治双线性系统的iISS准则。最后，通过算例说明了所得结果的适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.