<i>D^α</i>‐Type Iterative Learning Control for Fractional‐Order Linear Time‐Delay Systems

Abstract

Abstract This paper presents a second order ‐type iterative learning control ( ILC ) scheme for a class of fractional‐order linear time‐delay systems with fractional order α (0 ≤ α &lt; 1). First, by analyzing the control and learning processes, a discrete system for ‐type ILC is established. Then, ILC design problem is converted to a stabilization problem for such a discrete system. Next, by introducing the ( λ , ξ )‐norm and using a generalized Gronwall‐Bellman lemma, the sufficient condition for the robust convergence with respect to the bounded external disturbance of the control input and the tracking errors is obtained. Finally, the validity of the method is verified by two numerical examples.