Discrete Output Regulator Design for the Linearized Saint–Venant–Exner Model

Abstract

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.

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“…The proof of the Lemma above was shown in previous contributions. 30 Thus, the following assumption is made:…”

“…The proof of the Lemma above was shown in previous contributions 30 . Thus, the following assumption is made:Assumption A small enough value of Δ t is used such that the discrete‐time representation of the system shown in Equation () is a good approximation of the open‐loop system internal dynamics and the finite set of input/output relations.…”