Affiliation:
1. College of Computer Science, Chengdu University, Chengdu, Sichuan, China
Abstract
In this paper, we investigate the observability of the fractional resolvent family, and we prove two main results: the first result shows a generalization of the Hautus-type test for observable exponentially stable semigroups to the fractional resolvent family and the second result shows the equivalence of the observability and the below boundedness of the linear operator on the wave packet when the generator conforms to a specific form.
Funder
National Natural Science Foundation of China
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