INPUT-TO-STATE STABILITY FOR BILINEAR FEEDBACK SYSTEMS

被引：0

作者：

Hosfeld, Rene ^{[1
,2
]}

Jacob, Birgit ^{[1
]}

Schwenninger, Felix l. ^{[3
]}

Tucsnak, Marius ^{[4
]}

机构：

[1] Univ Wuppertal, Sch Math & Nat Siences, IMACM, Gausstr 20, D-42119 Wuppertal, Germany

[2] Univ Hamburg, Dept Math, Bundesstr 55, D-20146 Hamburg, Germany

[3] Univ Twente, Dept Appl Math, POB 217, NL-7500 AE Enschede, Netherlands

[4] Univ Bordeaux, Inst Math Bordeaux, 351 Cours Liberat, F-33405 Talence, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2024年 / 62卷 / 03期

关键词：

bilinear systems; feedback systems; C; 0-semigroups; admis sibility; LYAPUNOV FUNCTIONS; BURGERS-EQUATION; PARABOLIC PDES; BOUNDARY; STABILIZATION; ISS;

D O I：

10.1137/23M155788X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

where all appearing operators are possibly unbounded. The precise setting is introduced in section 2. This abstract class of evolution equations covers numerous partial differential equations such as the Navier-Stokes equation, the Burgers equation, or wave type equations, which will serve as examples for the theory developed in this note. By regarding (1.1) as a linear system with bilinear feedback N(z,y), we will prove that for ``small"" initial values z0 and input functions u : [0, t] - U, there exists a unique (mild) solution z(center dot) of (1.1), which satisfies the following stability-robustness estimate:

引用

页码：1369 / 1389

页数：21

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