Gugat M (2025)
Publication Type: Journal article, Original article
Publication year: 2025
Book Volume: 63
Pages Range: 452--471
Journal Issue: 1
DOI: 10.1137/24M1648570
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.
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.
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