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Controllability and stability of a second-order hyperbolic system with collocated sensor/actuator. (English) Zbl 0994.93021

Summary: A second-order hyperbolic system with collocated sensor/actuator is considered. The semigroup generation is shown for the closed-loop system under the feedback with 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. An example of a beam equation is presented to display the application.

MSC:

93C20 Control/observation systems governed by partial differential equations
93B05 Controllability
93D15 Stabilization of systems by feedback
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