This manuscript addresses the regulator design in the discrete-time setting for the unstable linearized Saint–Venant–Exner model, which describes the dynamics of a sediment-filled water canal. The proposed regulator ensures the closed-loop stability and proper tracking of polynomial and periodic reference signals using output feedback in a sample-data setting. To design this regulator, the system discrete representation is achieved by the application of the structure-preserving Cayley-Tustin time discretization and the direct relation with the regulator in the continuous-time setting is shown. The regulator design in the continuous-time setting is developed using the backstepping methodology ensuring the closed-loop stability and the observer design, while the Sylvester equations are solved to achieve proper tracking. Finally, the numerical simulation results are presented to show the performance of the regulator.

中文翻译：

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线性化Saint-Venant-Exner模型的离散输出调节器设计

该手稿介绍了不稳定线性化Saint-Venant-Exner模型在离散时间设置中的调节器设计，该模型描述了充满沉积物的水渠的动力学。所提出的调节器可在样本数据设置中使用输出反馈来确保闭环稳定性以及多项式和周期性参考信号的正确跟踪。为了设计该调节器，通过应用保留结构的Cayley-Tustin时间离散化来实现系统离散表示，并显示了在连续时间设置中与调节器的直接关系。连续时间设置中的调节器设计是使用反推方法开发的，以确保闭环稳定性和观察者设计，同时对Sylvester方程进行求解以实现正确的跟踪。最后，