Boundary stabilization of quasi-linear hyperbolic systems with varying time delay

Gugat M (2025)


Publication Type: Journal article, Original article

Publication year: 2025

Journal

Book Volume: 63

Pages Range: 452--471

Journal Issue: 1

DOI: 10.1137/24M1648570

Abstract

In this paper we consider the boundary feedback stabilization of a quasi-linear hy-

perbolic system of balance laws. At one end of the space interval, there is a reflecting boundary

condition. At the other end a stabilizing feedback law with a varying time-delay is prescribed. We

present sufficient conditions for the exponential stability of the system. We show that exponential

stabilization is possible if the product of the length of the interval and an upper bound for the source

term is sufficiently small. We also show that if the product of the length of the interval and a lower

bound for the source term is sufficiently large, the system is unstable. Our analysis is based on Lya-

punov functions with weights that are given by hyperbolic functions that generalize the well-known

exponential weights. Compared with previous contributions, we obtain conditions that can be veri-

fied more easily in terms of the system parameters. Our results show that for sufficiently short space

intervals, and also with varying time-delay, exponential stabilization is possible with appropriately

chosen feedback gains that depend on the maximal value of the time-delay and the maximal absolute

value of its derivative.

Authors with CRIS profile

How to cite

APA:

Gugat, M. (2025). Boundary stabilization of quasi-linear hyperbolic systems with varying time delay. SIAM Journal on Control and Optimization, 63(1), 452--471. https://doi.org/10.1137/24M1648570

MLA:

Gugat, Martin. "Boundary stabilization of quasi-linear hyperbolic systems with varying time delay." SIAM Journal on Control and Optimization 63.1 (2025): 452--471.

BibTeX: Download