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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 410292, 11 pages
http://dx.doi.org/10.1155/2015/410292
Research Article

A PD-Type Iterative Learning Control for a Class of Switched Discrete-Time Systems with Model Uncertainties and External Noises

Department of Applied Mathematics, School of Mathematics and Statistics, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, Shaanxi 710049, China

Received 25 March 2015; Revised 27 May 2015; Accepted 9 June 2015

Academic Editor: Manuel De la Sen

Copyright © 2015 Xuan Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A PD-type iterative learning control algorithm is applied to a class of linear discrete-time switched systems for tracking desired trajectories. The application is based on assumption that the switched systems repetitively operate over a finite time interval and the switching rules are arbitrarily prespecified. By taking advantage of the super-vector approach, a sufficient condition of the monotone convergence of the algorithm is deduced when both the model uncertainties and the external noises are absent. Then the robust monotone convergence is analyzed when the model uncertainties are present and the robustness against the bounded external noises is discussed. The analysis manifests that the proposed PD-type iterative learning control algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily preset switching rules. The attached simulations support the feasibility and the effectiveness.