Controllability and stability of a second-order hyperbolic system with collocated sensor/actuator

@article{Guo2002ControllabilityAS,
  title={Controllability and stability of a second-order hyperbolic system with collocated sensor/actuator},
  author={Bao-Zhu Guo and Yue-Hu Luo},
  journal={Systems & Control Letters},
  year={2002},
  volume={46},
  pages={45-65}
}
A second-order hyperbolic system with collocated sensor=actuator is considered. The semigroup generation is shown for the closed-loop system under the feedback of a generic unbounded observation operator. The equivalence between the exponential stability of the closed-loop system and exact controllability of the open-loop system is established in the general framework of well-posed linear systems. Finally, the conditions are weakened for the diagonal semigroups with 6nite dimensional inputs… CONTINUE READING

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