LMI Stability Conditions for Nabla Fractional Order Systems With Order α ∈ (0, 2)

This brief deals with the stability of nabla fractional order systems with order belonging to (0, 2). Due to the complexity of the stable region, a subset is constructed via a clustering region. From this, the stability conditions are formulated in terms of LMIs, which are sufficient and necessary to evaluate all the eigenvalues of system matrix locating at the approximation region. Besides the strict theoretical proof, two numerical examples are provided to verify the validity of the elaborated results.