New approach to output feedback control of fractional-order linear systems with positive real uncertainty

This paper concerns with the static output feedback stabilisation of uncertain fractional-order linear systems. To solve the static output problem via linear matrix inequality approach, a new separation technique is adopted to separate the controller gain matrices from Lyapunov variable. Based on this method, the sufficient conditions for robust asymptotical stability of the closed-loop systems are established. Unlike previous methods, the proposed methods do not need equality constraints and consider an iterative search of the controller. A numerical example is provided to illustrate the validity of the proposed methods.