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Journal of Applied Nonlinear Dynamics 8(3) (2019) 447--461 | 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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