Observer‐based stabilisation of a class of fractional order non‐linear systems for 0 < α <2 case

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.