Abstract
In this paper, we consider the question of the state fractional spatial derivative stabilization, using Riemann–Liouville derivative of order \(\alpha \in ]0, 1[\), for a class of bilinear distributed systems. Firstly, we characterize the feedback control that ensure the strong and the weak stabilization of the fractional output. Then, we solve a minimization fractional problem. Finally, we provide an example with numerical simulations to illustrate the effectiveness of the given stabilization theorems.
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