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Proceedings of the American Mathematical Society

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Contraction semigroups, stabilization, and the mean ergodic theorem

Author: Robert E. O’Brien
Journal: Proc. Amer. Math. Soc. 71 (1978), 89-94
MSC: Primary 93D15
MathSciNet review: 495844
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Abstract: Consider the semidynamical system, $ \dot x = Ax + Bu$, where A generates a $ {C_0}$-contraction semigroup and B is bounded. If the system is controllable then it is weakly stabilizable. If in addition the semigroup is quasi-compact and B is compact, the mean ergodic theorem implies that the stability is uniform and exponential.

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Keywords: Contraction semigroup, controllability, stabilization
Article copyright: © Copyright 1978 American Mathematical Society