A High-order Iterative Learning Control for Discrete-Time Linear Switched Systems

In this paper, a high-order iterative learning control (ILC) scheme is proposed for discrete-time linear switched systems with iteration-varying factors (e.g. reference trajectories, initial states and disturbances). The iteration-varying factors of initial states here mean the resetting errors which may exist at the beginning of each pass due to the poor repetitiveness of the system. Firstly, a high-order ILC law embedding the characteristic of known variation of the reference trajectories is introduced to the system. In order to handle the iteration-varying factors, a Lyapunov-Krasovskii function is proposed and sufficient conditions for exponential stability with $l_{2}$ performance of the system are derived in the form of a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed results.