Abstract
This study focuses on the global asymptotic stability and observer-based stabilisation problems of a class of fractional order non-linear systems with the fractional order 0 < α < 2. Based on the decay properties of the Mittag–Leffler function and the Gronwall–Bellman inequality, two sufficient conditions on the global asymptotic stability of fractional order non-linear systems are derived for the fractional order 0 < α < 1 and 1 < α < 2, respectively. According to the proposed conditions, an iterative algorithm is presented to design the fractional order non-linear observer and estimated state feedback control law. Finally, two numerical examples illustrate the advantages of the proposed iterative algorithm.
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