Gugat M (2024)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2024
Book Volume: 53
Pages Range: 163-187
Journal Issue: 1
URI: https://sciendo.com/de/article/10.2478/candc-2024-0008
Open Access Link: https://sciendo.com/de/article/10.2478/candc-2024-0008
Lyapunov functions with exponential weights have
been used successfully as a powerful tool for the stability analysis
of hyperbolic systems of balance laws. In this paper we extend the
class of weight functions to a family of hyperbolic functions and
study the advantages in the analysis of 2 × 2 systems of balance
laws. We present cases connected with the study of the limit of
stabilizability, where the new weights provide Lyapunov functions
that show exponential stability for a larger set of problem parameters
than classical exponential weights.
Moreover, we show that sufficiently large time-delays influence
the limit of stabilizability in the sense that the parameter set, for
which the system can be stabilized becomes substantially smaller.
We also demonstrate that the hyperbolic weights are useful in
the analysis of the boundary feedback stability of systems of balance
laws that are governed by quasilinear hyperbolic partial differential
equations
APA:
Gugat, M. (2024). New Lyapunov functions for systems with source terms. Control and Cybernetics, 53(1), 163-187. https://doi.org/10.2478/candc-2024-008
MLA:
Gugat, Martin. "New Lyapunov functions for systems with source terms." Control and Cybernetics 53.1 (2024): 163-187.
BibTeX: Download