Second-order P-type iterative learning control for fractional order non-linear time-delay systems

This paper presents a second-order P-type iterative learning control (ILC) scheme for a class of fractional-order non-linear time-delay systems with fractional order alpha (0 <= alpha < 1). First, by analysing the control and learning processes, a discrete system for P-type ILC is established and the ILC design problem is then converted to a stabilisation problem for such a discrete system. Next, by introducing the (Lambda, xi)-norm and using a generalised Gronwall-Bellman lemma, the sufficient condition for the convergence of the control input and the tracking errors is obtained. Finally, the validity of the method is verified by a numerical example.