Flatness based feedback design for hyperbolic distributed parameter systems with spatially varying coefficients

State feedback design for a hybrid system consisting of a spatially one-dimensional second order hyperbolic distributed parameter system with spatially dependent coefficients and a finite dimensional linear system is considered. The approach relies on the flatness based parametrization of the solutions which is obtained by integration along the characteristics. Based on this parametrization the design of flatness based feedback controllers is proposed in order to achieve an arbitrary desired closed loop dynamics. Approximation strategies of the obtained infinite dimensional control laws are proposed.