Robust stability and stabilization of multi‐order fractional‐order systems with interval uncertainties: An LMI approach

Abstract

Abstract This paper concentrates on the robust stability and stabilization problems of multi‐order fractional‐order systems (MOFOSs) with interval uncertainties. Firstly, the new sufficient conditions for the stability of the nominal systems are given, which are suitable for robust analysis and controller design. Then, based on the above stability conditions, the robust stability conditions for the uncertain systems are proposed. Secondly, in order to stabilize the nominal systems and uncertain systems, the state feedback controllers are designed. All the results are in the form of linear matrix inequalities and can be applied in incommensurate cases. Finally, some numerical examples are provided to verify the effectiveness of our results.