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Summary In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are proposed to the finite‐time stability of the system with the fractional order. Numerical results are given and compared with other published data in the literature to demonstrate the validity of the proposed theoretical results.

In this paper, the problem of a global practical Mittag Leffler feedback stabilization for a class of nonlinear fractional order systems by means of observer is described. The linear matrix inequality approach is used to guarantee the practical stability of the proposed feedback fractional order system. An illustrative example is given to show the applicability of the results.

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The observer design problem for integer-order systems has been the subject of several studies. However, much less interest has been given to the more general fractional-order systems, where the fractional-order derivative is between 0 and 1. In this paper, a particular form of observers for integer-order Lipschitz, one-sided Lipschitz and quasi-one-sided Lipschitz systems, is extended to the fractional-order calculus. Then, the obtained states estimates are used for an eventual feedback control, and the separation principle is tackled. The effectiveness of the proposed scheme is shown through simulation for two numerical examples.

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