# 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={B. Guo and Y. Luo}, journal={Syst. Control. Lett.}, 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 finite dimensional inputs… CONTINUE READING

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