  The problem of state estimation for a system of coupled hyperbolic PDEs and
ODEs with Lipschitz nonlinearities with boundary measurements is considered. An
infinite dimensional observer with a linear boundary injection term is used to
solve the state estimation problem. The interconnection of the observer and the
system is written in estimation error coordinates and analyzed as an abstract
dynamical system. The observer is designed to achieve global exponential
stability of estimation error with respect to a suitable norm. Sufficient
conditions in the form of matrix inequalities are proposed to design the
observer. Numerical simulations support and corroborate the theoretical
results.
