Contents Online
Methods and Applications of Analysis
Volume 26 (2019)
Number 2
Special Issue in Honor of Roland Glowinski (Part 1 of 2)
Guest Editors: Xiaoping Wang (Hong Kong University of Science and Technology) and Xiaoming Yuan (The University of Hong Kong)
Exponential stability of PI control for Saint-Venant equations with a friction term
Pages: 101 – 112
DOI: https://dx.doi.org/10.4310/MAA.2019.v26.n2.a1
Authors
Abstract
We consider open channels represented by Saint-Venant equations that are monitored and controlled at the downstream boundary and subject to unmeasured flow disturbances at the upstream boundary. We address the issue of feedback stabilization and disturbance rejection under Proportional-Integral (PI) boundary control. For channels with uniform steady states, the analysis has been carried out previously in the literature with spectral methods as well as with Lyapunov functions in Riemann coordinates. In this article, our main contribution is to show how the analysis can be extended to channels with non-uniform steady states with a Lyapunov function in physical coordinates.
Keywords
hyperbolic systems, boundary control, Lyapunov stability, Saint-Venant equations
2010 Mathematics Subject Classification
35F61, 93D15, 93D30
Dedicated to Roland Glowinski, a master and a friend, on the occasion of his 80th birthday
Received 1 March 2018
Accepted 12 April 2019
Published 2 April 2020