Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System

Abstract EN

This paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay.

Firstly, we put forward a feedback flow control subject to the action of a constant time delay.

Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an energy space.

Subsequently, we deal with the eigenvalue problem of the system.

More importantly, exponential decay of solutions of the closed-loop system is derived provided that the feedback gain of the control is bounded.

Finally, the theoretical findings are validated via a set of numerical results.