On the stability of a star-shaped network of variable coefficients strings under joint damping

Boughamda, Walid

doi:10.1007/s00033-022-01727-7

Cited by 1 publication

(1 citation statement)

References 28 publications

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“…Till now, there are a growing number of works on the controllability and stability of star-shaped networks, and the control strategies are mainly based on boundary feedback control. 14,15 A system of N Korteweg-de Vries equations coupled by the boundary conditions has appeared in different contexts to describe propagation phenomena, where the configuration is also a star-shaped network, and the boundary inputs can act on a central node and on the N external nodes. By using ( N + 1 ) controls, the authors in Ammari and Crépeau 16 obtained stabilization and controllability results for a KdV system posed on a star-shaped network.…”

Section: Introductionmentioning

confidence: 99%

The PDP feedback control design and exponential stability for a star-shaped network of open channels

Zhao

Pang

Guo

et al. 2023

Advances in Mechanical Engineering

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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 [Formula: see text] channels with [Formula: see text] 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.

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