Observation and sliding mode observer for nonlinear fractional-order system with unknown input
Nadia Djeghali1, Said Djennoune1, Maamar Bettayeb2
1Laboratoire de Conception et Conduite des Systèmes de Production, University Mouloud Mammeri, Tizi-Ouzou, Algeria.
Abstract:
The main purpose of this paper is twofold. First, the observability and the left invertibility properties and the observable canonical form for nonlinear fractional-order systems are introduced. By using a transformation, we show that these properties can be deduced from an equivalent nonlinear integer-order system. Second, a step by step sliding mode observer for fault detection and estimation in nonlinear fractional-order systems is proposed. Starting with a chained fractional-order integrators form, a step by step first-order sliding mode observer is designed. The finite time convergence of the observer is established by using Lyapunov stability theory. A numerical example is given to illustrate the performance of the proposed approach.
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