The PDP feedback control design and exponential stability for a star-shaped network of open channels
The PDP feedback control design and exponential stability for a star-shaped network of open channels
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DOI：
10.1177/16878132231156056
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发表时间：
2023-02
影响因子：
2.1
通讯作者：
Dong‐xia Zhao;Yuting Pang;Yaping Guo;Junmin Wang
中科院分区：
文献类型：
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作者：
Dong‐xia Zhao;Yuting Pang;Yaping Guo;Junmin Wang
本文研究了星形明渠网络在位置和延迟位置（PDP）反馈控制器作用下的稳定性。首先，我们处理了单通道的特殊情况，并利用半群理论和严格的李雅普诺夫函数建立了闭环系统的适定性和指数稳定性。给出了系统参数和时滞的显式耗散条件。然后利用特征线法分析了闭环系统的时滞无关稳定性。接下来，我们将PDP控制设计扩展到具有n-1个入口通道和一个出口通道的n个通道的星形网络，并且可以类似地获得指数稳定性。最后，我们给出了三个通道的特殊情况下的一些数值模拟。
This paper investigates the stability of a star-shaped network of open channels under the position and delayed position (PDP) feedback controller. Firstly, we deal with the special case of a single channel, and the well-posedness and exponential stability of the closed-loop system are established by using the semi-group theory and a strict Lyapunov function. The explicit dissipative conditions for system parameters and time-delay are presented. Then, we analyze the delay-independent stability of the closed-loop system by the method of characteristic. Next, we extend the PDP control design to the star-shaped network of n channels with n − 1 inlet channels and one outlet channel, and the exponential stability can be obtained similarly. Finally, we give some numerical simulations for the special case of three channels.