  Hyperbolic systems in one dimensional space are frequently used in modeling
of many physical systems. In our recent works, we introduced time independent
feedbacks leading to the finite stabilization for the optimal time of
homogeneous linear and quasilinear hyperbolic systems. In this work, we present
Lyapunov's functions for these feedbacks and use estimates for Lyapunov's
functions to rediscover the finite stabilization results.
