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：
暂无
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
收藏
页码：1369 / 1389
页数：21
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