Journal of Applied Nonlinear Dynamics
Riemann Liouville Fractional Spatial Derivative Stabilization of Bilinear Distributed Systems
Journal of Applied Nonlinear Dynamics 8(3) (2019) 447461  DOI:10.5890/JAND.2019.09.008
Hanaa Zitane, Rachid Larhrissi, Ali Boutoulout
MACS Laboratory, Department of Mathematics, Faculty of Sciences, University of Moulay Ismail, Meknes, Morocco
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Abstract
The goal of this paper is to study a fractional output stabilization problem: the stabilization of the state fractional spatial derivative of complex purely imaginary order i α with α ∈]0,1[, for bilinear distributed systems. Firstly, we develop suﬃcient conditions for exponential, strong and weak fractional output stabilization for the considered system, also, we oﬀer some examples illustrating the obtained results. Moreover, we characterise the stabilizing control which minimizes an appropriate cost. Finally, an illustrating example with numerical simulations is given.
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