On $L_\infty$ Stabilization of Diagonal Semilinear Hyperbolic Systems by Saturated Boundary Control

International audienceThis paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities coupled with a nonlinear source term. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L 2 ([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local L ∞ exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given