A smoothing property of a hyperbolic system and boundary controllability

We investigate a method with which one can deduce controllability results from smoothing properties. Previous applications of the method were for partial differential equations like the Euler–Bernoulli Beam Equation (Petrowski-hyperbolic). In this paper we study the methodʹs applicability to a strictly hyperbolic system by considering the boundary controllability of a vibrating Timoshenko beam with physical characteristics that may vary along the length of the beam. Two cases are considered: A beam which is clamped at one end, the other end being controlled by a torque and transverse force; and a beam which is hinged at one end, where a control torque is applied, and free at the other end, where a control force is applied.