A Unified Framework of Stability Theorems for LTI Fractional Order Systems With 0 < α < 2

This brief aims to provide a set of criteria to ensure the stability or stabilization of a class of fractional order systems (FOS) for a given order α that belongs to the interval (0, 2). These criteria are based on a unified structure of linear matrix inequalities (LMIs). Their add-value manifests in involving the least real decision variables of LMIs and presenting a unified LMI formulation with order between zero and two. Those criteria are necessary and sufficient conditions that can be straightforward used to solve the feasible solutions with LMI toolbox. Finally, it yields numerical examples to highlight the efficiency of the proposed pseudo-state state feedback controller, where some comparisons with the previous stabilization criteria for FOS are given to show its less conservatism.