| Abstract: |
| By building up a type of observability inequality related to partial $L^2$-null approximate controllability of heat equation with time-invariant control, this work constructs a type of output feedback law of sampled-data form for rapid stabilization of heat equation with potential. Moreover, we get the both the lower and upper bounds of the norm of the feedback operator with respect to the sampling period. We find that the norm of the feedback will go to infinity when the sampling period goes to infinity or zero. Furthermore, we show that the norm of the feedback continuously depends on the sampling period, and there exists an optimal sampling period in the sense that the norm of the corresponding feedback is minimal. |
|