Riemann Liouville Fractional Spatial Derivative Stabilization of Bilinear Distributed Systems

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.