Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 56, Issue 1, Pages 75-101Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1048999
Keywords
time fractional reaction diffusion equation; boundary control; output feedback; stabilization
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Funding
- Israel Science Foundation [800/14]
- National Natural Science Foundation of China [61273129]
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In this paper, we consider boundary feedback stabilization for unstable time fractional reaction diffusion equations. New state feedback controls with actuation on one end are designed by the backstepping method for both Dirichlet and Neumann boundary controls. By the Riesz basis approach and the fractional Lyapunov method, we prove the existence and uniqueness and the Mittag-Leffler stability for the closed-loop systems. For both cases, the observers and the observer based output feedback are designed to stabilize the systems.
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