Semi-uniform input-to-state stability of infinite-dimensional systems
Semi-uniform input-to-state stability of infinite-dimensional systems
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DOI：
10.1007/s00498-022-00326-1
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发表时间：
2021-06
期刊：
影响因子：
--
通讯作者：
M. Wakaiki
中科院分区：
文献类型：
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作者：
M. Wakaiki
我们介绍了无限维系统的半均匀输入状态稳定性及其子类多项式输入状态稳定性的概念。我们基于均匀情况下的吸引力特性建立了半均匀输入状态稳定性的表征。提供了线性系统多项式输入状态稳定的充分条件，这根据半群乘积的多项式衰减率及其生成器的求解来限制输入算子的范围。我们还证明了一类双线性系统在非线性算子的一定平滑度假设下是多项式积分输入状态稳定的。
We introduce the notions of semi-uniform input-to-state stability and its subclass, polynomial input-to-state stability, for infinite-dimensional systems. We establish a characterization of semi-uniform input-to-state stability based on attractivity properties as in the uniform case. Sufficient conditions for linear systems to be polynomially input-to-state stable are provided, which restrict the range of the input operator depending on the rate of polynomial decay of the product of the semigroup and the resolvent of its generator. We also show that a class of bilinear systems are polynomially integral input-to-state stable under a certain smoothness assumption on nonlinear operators.