An LMI Approach to Resilient Fractional Order Observer Design for Lipschitz Fractional Order Nonlinear Systems Using Continuous Frequency Distribution

Amini Boroujeni, Elham; Momeni, Hamid Reza; Sojoodi, Mahdi

An LMI Approach to Resilient Fractional Order Observer Design for Lipschitz Fractional Order Nonlinear Systems Using Continuous Frequency Distribution

Authors

E. Amini Boroujeni ¹

H. R. Momeni ²

M. Sojoodi ³

¹ Assistant Professor, Electrical and Computer Engineering Department, Kharazmi University, Tehran, Iran,:

² Associated Professor, Faculty of Electrical Engineering, Tarbiat Modares University, Tehran, Iran

³ .Assistant Professor, Faculty of Electrical Engineering, Tarbiat Modares University, Tehran, Iran

Abstract

Non-fragile observer design is the main problem of this paper. Using continuous frequency distribution, the stability conditions based on integer order Lyapunov theorem are derived for Lipschitz class of nonlinear fractional order systems. The proposed observer is stable beside the existence of both gain perturbation and input disturbance. For the first time, in this paper a systematic method is suggested based on linear matrix inequality to find an optimal observer gain to minimize both the effects of disturbance on the synchronization error and norm of the observer gain. A comparison has done between this observer and previous research on resilient observer design for nonlinear fractional order systems based on fractional order Lyapunov method. The comparison shows a much broader range of feasible response for the proposed method of this paper besides simpler computing. After presenting thediscussion, chaos synchronization is simulated to show the effectiveness of the proposed method in the end.

Keywords

Continues frequency distribution

fractional order observer

Linearmatrix inequality

Lipchitz nonlinear systems

Resilient observer