CONTRACTION ANALYSIS OF VOLTERRA INTEGRAL EQUATIONS VIA REALIZATION THEORY AND FREQUENCY-DOMAIN METHODS

被引：0

作者：

V. Kudryashova, Elena ^{[1
]}

Reitmann, Volker ^{[1
]}

机构：

[1] St Petersburg State Univ, Dept Math & Mech, St Petersburg, Russia

来源：

JOURNAL OF COMPUTATIONAL DYNAMICS | 2023年 / 10卷 / 01期

关键词：

STABILITY; SYSTEMS;

D O I：

10.3934/jcd.2022020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Realization theory for linear input-output operators and frequency domain methods for the solvability of Riccati operator equations are used for the contraction analysis of a class of nonlinear Volterra integral equations in some Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in some weighted Sobolev space which has the same stability properties as the Volterra equation.

引用

页码：248 / 267

页数：20

共 20 条

[1]

[Anonymous], 1987, Partial differential equations

[2]

[Anonymous], 1971, Die Grundlehren der mathematischen Wissenschaften

[3] DYNAMIC PROGRAMMING [J].

BELLMAN, R .

SCIENCE, 1966, 153 (3731) :34-&

[4]

BEREZANSKII YM, 1965, EIGENFUNCTION EXPANS

[5]

Brusin V. A., 1977, SIB MAT ZH, V13, P1246

[6] EQUIPRESENCE AND CONSTITUTIVE EQUATIONS FOR RIGID HEAT CONDUCTORS [J].

COLEMAN, BD ;

GURTIN, ME .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1967, 18 (02) :199-&

[7]

Desoer CA, 2009, CLASS APPL MATH, V55, P1, DOI 10.1137/1.9780898719055

[8]

Gelig A. K., 1998, Stability and Oscillations of Nonlinear Pulse-modulated Systems, DOI DOI 10.1007/978-1-4612-1760-2

[9] Converse theorems on contraction metrics for an equilibrium [J].

Giesl, Peter .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 424 (02) :1380-1403

[10] ON ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF AN INTEGRO-DIFFERENTIAL EQUATION [J].

HALANAY, A .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1965, 10 (02) :319-&

← 1 2 →