Observer-based robust stabilisation of a class of non-linear fractional-order uncertain systems: an linear matrix inequalitie approach

This study focuses on the observer-based robust stabilisation problem of a class of non-linear fractional-order uncertain systems with admissible time-variant uncertainty and bounded perturbation on the observer gain. A sufficient condition for the robust asymptotic stability of the observer-based non-linear fractional-order uncertain systems is presented based on direct Lyapunov approach. Utilising the matrix´s singular value decomposition method (SVD), the systematic robust stabilisation design algorithm is then proposed. All the results are obtained in terms of linear matrix inequalities. A numerical example is provided to illustrate the efficiency and advantage of the proposed algorithm.