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

DOI:
https://doi.org/10.1090/S0002-9939-1978-0495844-2

MathSciNet review:
495844

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the semidynamical system, , where *A* generates a -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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0495844-2

Keywords:
Contraction semigroup,
controllability,
stabilization

Article copyright:
© Copyright 1978
American Mathematical Society