Robust normalization and stabilization of descriptor fractional‐order systems with polytopic uncertainties in all matrices

Abstract

AbstractThis paper addresses the robust normalization and stabilization problems for descriptor fractional‐order systems with polytopic uncertainties in all system coefficient matrices, including the state derivative coefficient matrix. Firstly, novel sufficient conditions for the robust normality and stability of polytopic uncertain descriptor fractional‐order systems are presented based on linear matrix inequalities. Then, for the cases when the uncertain parameters are known and unknown, the proportional and derivative state feedback control with constant feedback gain and parameter‐dependent feedback gain are introduced to normalize and stabilize such systems, respectively. Finally, numerical examples are provided to show that the proposed approach is effective and less conservative than the results obtained by other researchers.