Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 705346, 12 pages
http://dx.doi.org/10.1155/2011/705346
Research Article

Design of Switching Multiobjective Controller: A New Approach

Ahmad Fakharian1,2

1Department of Electrical and Computer Engineering, Islamic Azad University, Qazvin Branch, Nokhbegan Boulevard, P.O. Box 34185-1416, Qazvin, Iran
2Control Engineering Group, Department of Computer Science, Electrical and Space Engineering, Luleå University of Technology, 971 87 Luleå, Sweden

Received 11 February 2011; Revised 9 June 2011; Accepted 29 August 2011

Academic Editor: John Burns

Copyright © 2011 Ahmad Fakharian. 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

Design of switching 𝐻 2 / 𝐻 ∞ output-feedback controller for discrete-time LTI systems with state-multiplicative noise is considered. The closed loop system achieves a minimum bound on the stochastic 𝐻 2 performance level, while satisfying the 𝐻 ∞ performance. The proposed controller is based on a fuzzy supervisor which manages the combination of two separate 𝐻 2 and 𝐻 ∞ controllers. A convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to ensure a good performance in both the transient phase ( 𝐻 2 controller) and the steady phase ( 𝐻 ∞ controller). The stability analysis uses the Lyapunov technique, inspired from switching system theory, to prove that the closed loop system with the proposed controller structure remains globally stable despite the configuration changing.