Finite-time backstepping boundary stabilization of 3 × 3 hyperbolic systems

We consider the problem of boundary stabilization of 3 × 3 linear first-order hyperbolic systems with one positive and two negative transport speeds by using backstepping. The main result of the paper is to supplement the previous works on how to choose multi-boundary feedback inputs applied on the states corresponding to the negative velocities to obtain finite-time stabilization of the original system in the spatial L² sense. Our method is still valid for boundary stabilization of general n × n hyperbolic system with arbitrary numbers of states traveling in either directions. 2010 Mathematics Subject Classification. 93D15, 35L04.