Nonlinear Dynamics

, Volume 80, Issue 4, pp 1801–1810 | Cite as

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

Original Paper


In this paper, the stability of a nonlinear non-fragile \(H_\infty \) 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.


Financial system Iterative method Linear matrix inequality Lyapunov stability Non-fragility Robust nonlinear fractional-order observer 



The authors would like to thank Dr. Mahdi Pourgholi for his suggestions and criticism that helped in improving this paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Automation and Instruments Laboratory, Electrical Engineering DepartmentTarbiat Modares UniversityTehranIran

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