On hyperbolic systems associated with the modelling and control of vibrating networks

The authors describe a general model for vibrating networks and show how the model applies to networks of elastic strings or Timoshenko beams. They indicate how hyperbolic energy estimates for first-order systems yield the a priori estimates needed to prove exact controllability and stabilizability. They show how the model can be generalized to allow mixed networks of strings and beams. They also discuss generalizations of the Timoshenko beam and their relation on the present model