Learning ability analysis for linear discrete delay systems with iteration-varying trial length

Abstract

This study investigates finite-time tracking issues of linear discrete delay systems with iteration-varying trial length (IVTL). With the assistance of explicit solutions expressed by the discrete matrix delayed exponential emA⋅, the obstacle in explicitly expressing the tracking error is overcome. Iterative learning control (ILC) update laws using the current state feedback control are proposed to reduce greatly acute error jitter caused by IVTL. The convergence conditions are presented for realizable systems and learning ability of the delay systems. The relation between ‖emA⋅‖1 and probability distribution of the trial length is given to imply how to guarantee convergence of tracking error. Finally, a numerical simulation is presented to illustrate that the ILC scheme can improve transient tracking performance. Moreover, convergence speed of the delay systems can be expedited.