Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 341720, 22 pages
Research Article

Parameterized Regulator Synthesis for Bimodal Linear Systems Based on Bilinear Matrix Inequalities

Zhizheng Wu and Foued Ben Amara

Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, Canada

Received 3 July 2007; Revised 18 January 2008; Accepted 7 March 2008

Academic Editor: Tamas Kalmar-Nagy

Copyright © 2008 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.


A regulator design method is presented for switched bimodal linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. The switching in the bimodal system is defined by a switching surface. The regulator design approach consists of three steps. The first step is based on constructing a switched observer-based state feedback central controller for the switched linear system. The second step involves augmenting the switched central controller with additional dynamics to construct a parameterized set of switched controllers. In the third step, two sufficient regulation conditions are derived for the resulting switched closed loop system. The regulation conditions present guidelines for the selection of the additional dynamics used to parameterize the switched controllers to yield the desired regulator. A regulator synthesis approach is proposed based on solving properly formulated bilinear matrix inequalities. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.