Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 240204, 19 pages
Research Article

Output Regulation in Discrete-Time Switched Bimodal Systems Based on Youla Parameterized Stabilizing Controllers

1Department of Precision Mechanical Engineering, Shanghai University, 149 Yanchang Road, Shanghai 200072, China
2Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada M5S 3G8

Received 29 May 2012; Revised 28 August 2012; Accepted 3 September 2012

Academic Editor: Jitao Sun

Copyright © 2012 Zhizheng Wu and Foued Ben Amara. 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.


Motivated by a class of contact vibration control problems in mechanical systems, this paper considers a regulation problem for discrete-time switched bimodal linear systems where it is desired to achieve output regulation against partially known deterministic and unknown random exogenous signals. First, a set of observer-based Youla parameterized stabilizing controllers is constructed, based on which the regulation conditions for the switched system against the deterministic signals along with an performance constraint against the unknown random signals are derived. Then a corresponding regulator synthesis algorithm is developed based on solving properly formulated linear matrix inequalities. The proposed regulator is successfully evaluated on an experimental setup involving a switched bimodal mechanical system subject to contact vibrations, hence, demonstrating the effectiveness of the proposed regulation approach.