Contraction semigroups, stabilization, and the mean ergodic theorem

O’Brien, Robert E.

doi:10.1090/S0002-9939-1978-0495844-2

Contraction semigroups, stabilization, and the mean ergodic theorem
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Proc. Amer. Math. Soc. 71 (1978), 89-94 Request permission

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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