摘要
本文研究了一个复杂冗余系统的指数稳定性.通过分析系统算子的谱分布和估计系统算子预解式的范数,得到系统算子预解式的一致有界横坐标小于零.利用预解式的一致有界横坐标和半群增长界的关系,可知在零特征值的余子空间上,半群具有负的增长阶.由半群指数稳定等价于半群的增长界为负得到了本文的主要结论.
In this paper, the exponential stability of a complex redundant system is investigated. First, the abscissa of uniform boundedness of the resolvent of the system operator is less than zero, which is obtained through the spectral distribution of the system operator and an estimate for the norm of the resolvent. Second, the growth bound of the semigroups is less than zero on the complement of zero-eigenvalue subspace, which was further obtained by the relations of the abscissa of uniform boundedness and the resolvent of the system operator. Finally, the desired result is obtained since the exponential stability of the semigroups is equivalent to the negative growth bound.
出处
《数学进展》
CSCD
北大核心
2012年第6期713-722,共10页
Advances in Mathematics（China）
基金
国家自然科学基金(No.11101051)
关键词
冗余系统
c_0半群
增长界
指数稳定性
redundant system
co semigroups
growth bound
exponential stability
