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.