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Since is stable under disturbances from, we obtain (3.44).
We claim that is stable under disturbances from with respect to for.
Also, he showed that total stability implies stability under disturbances from hull in [1, Theorem 1].
This shows that is stable under disturbances from with respect to.
from the fact that is stable under disturbances from with respect to.
This shows that is stable under disturbances from with respect to for.
To have optimal response under disturbances, adaptive schemes appear to be a particularly attractive choice.
He showed that for a periodic integro-differential equation, uniform stability and stability under disturbances from hull are equivalent.
Note that total stability implies stability under disturbances from hull for (2.7) in view of Theorem 3.8.
The concept of stability under disturbances from hull was introduced by Sell [16, 17] for the ordinary differential equation.
Hamaya [1] discussed the relationship between stability under disturbances from hull and total stability for the integro-differential equation (1.1).
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