Exponential stability of perturbed superstable systems in Hilbert spaces

被引：1
作者：
Chen, Jian-Hua [1 ]
Yi, Nian-Yu [2 ]
Li, Yong-Yao [3 ]
机构：
[1] Hunan Univ Sci & Technol, Sch Math & Computat Sci, Xiangtan 411201, Peoples R China
[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China
[3] Foshan Univ, Sch Phys & Optoelect Engn, Foshan 528000, Peoples R China
来源：
SEMIGROUP FORUM | 2018年 / 96卷 / 01期
关键词：
Operator semigroup; Superstability; Exponential stability; Weyl spectrum; Essential spectrum; STRONGLY CONTINUOUS SEMIGROUPS; SPECTRAL MAPPING-THEOREM; LINEAR-SYSTEMS;
D O I：
10.1007/s00233-017-9865-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study exponential stability of superstable systems in Hilbert spaces under perturbations. Formulas to calculate or to estimate the exponential growth bound of the perturbed systems are derived via which sufficient conditions on exponential stability are established. The obtained results are applied to a partial differential equation governing the vibration of a smart beam made of self-straining material. Several numerical simulations are given.
引用
收藏
页码：126 / 141
页数：16
相关论文
共 30 条
  • [1] A SPECTRAL MAPPING-THEOREM FOR PERTURBED STRONGLY CONTINUOUS SEMIGROUPS
    ANDREU, F
    MARTINEZ, J
    MAZON, JM
    [J]. MATHEMATISCHE ANNALEN, 1991, 291 (03) : 453 - 462
  • [2] [Anonymous], 1971, Linear operators. Part 3: Spectral operators
  • [3] [Anonymous], GTM
  • [4] [Anonymous], 1996, INTRO SPECTRAL THEOR
  • [5] Balakrishnan A., 2012, AEROELASTICITY
  • [6] Balakrishnan A. V., 1997, 18 IFIP TC7 C SYST M
  • [7] Balakrishnan A.V., 2001, LECT NOTES PURE APPL
  • [8] Superstability of systems
    Balakrishnan, AV
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2005, 164 (02) : 321 - 326
  • [9] BALAKRISHNAN AV, 1997, 1 INT C NONL PROBL A
  • [10] BALAKRISHNAN AV, 1996, DYNAMIC SYSTEMS APPL, V5, P371
123