  We present a control design for semilinear and quasilinear 2x2 hyperbolic
partial differential equations with the control input at one boundary and a
nonlinear ordinary differential equation coupled to the other. The controller
can be designed to asymptotically stabilize the system at an equilibrium or
relative to a reference signal. Two related but different controllers for
semilinear and general quasilinear systems are presented and the additional
challenges in quasilinear systems are discussed. Moreover, we present an
observer that estimates the distributed PDE state and the unmeasured ODE state
from measurements at the actuated boundary only, which can be used to also
solve the output feedback control problem.
