论文标题
无限尺寸caputo时间分数差分线性系统的稳定性和稳定
The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems
论文作者
论文摘要
我们研究了带有Caputo衍生物的希尔伯特空间中无限尺寸尺寸分数线性系统的稳定性和稳定概念。首先，基于强烈连续的半群和概率密度函数产生的运算符家族，我们为所考虑的系统类别的指数稳定性提供了足够和必要的条件。然后，通过假设系统动力学是对称和均匀椭圆形的，并且通过使用Mittag-Leffler函数的性质，我们提供了足够的条件来确保稳定的稳定性。最后，我们表征了一个明确的反馈控制，该反馈控制可以通过分解方法确保受控的Caputo时间分数线性系统的强稳定。提出了一些示例，以说明我们结果的有效性。
We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provide sufficient and necessary conditions for the exponential stability of the considered class of systems. Then, by assuming that the system dynamics is symmetric and uniformly elliptic and by using the properties of the Mittag-Leffler function, we provide sufficient conditions that ensure strong stability. Finally, we characterize an explicit feedback control that guarantees the strong stabilization of a controlled Caputo time fractional linear system through a decomposition approach. Some examples are presented that illustrate the effectiveness of our results.
