An iterative method to design optimal non-fragile $${\varvec{H}}_{\varvec{\infty }}$$H∞ observer for Lipschitz nonlinear fractional-order systems

In this paper, the stability of a nonlinear non-fragile $$H_\infty $$H∞ fractional-order observer, based on the fractional-order Lyapunov theorem, is investigated in detail. It is the first time to derive the optimal gain of desired observer among a solution set that satisfies the nonlinear robust non-fragile fractional-order observer stability conditions systematically using linear matrix inequality approach. An iterative linear matrix inequality algorithm is introduced while a boundary condition is unknown during the design procedure. Finally, a fractional-order financial system is introduced to show the effectiveness of the proposed method. It has been shown that not only the iterative method is successful to find the proper boundary condition, but also the performance of the proposed observer is satisfying both non-fragility and robustness to external disturbances with an acceptable accuracy.

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