An analysis and design method for fractional-order linear systems subject to actuator saturation and disturbance

In this paper, two methods are proposed for investigating stability of fractional‐order systems under saturated linear feedback. The first stability condition can be used for fractional‐order linear systems with nonlinear element that is Lipschitz in state. The second stability condition has been achieved by exploring the special property of saturation using an auxiliary feedback matrix. For comparison of the two analyses, domains of attraction are applied using the proposed optimizations whose conditions can be expressed as Linear Matrix Inequalities in terms of all the varying parameters hence being appropriate for controller synthesis. Furthermore, the stability condition is achieved with regard to persistence disturbance. It is employed for determining the invariant sets of the given system by the proposed optimization problems. The results of the proposed analysis and methods are illustrated by three examples.