Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 903126, 28 pages
doi:10.1155/2011/903126
Research Article

On Output Feedback Multiobjective Control for Singularly Perturbed Systems

Control and Communication Networks Laboratory, Electrical Engineering Department, Tarbiat Modares University, Tehran, Iran

Received 6 September 2010; Revised 30 November 2010; Accepted 6 January 2011

Academic Editor: Alexei Mailybaev

Copyright © 2011 Mehdi Ghasem Moghadam and Mohammad Taghi Hamidi Beheshti. 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 new design procedure for a robust 𝐻 2 and 𝐻 control of continuous-time singularly perturbed systems via dynamic output feedback is presented. By formulating all objectives in terms of a common Lyapunov function, the controller will be designed through solving a set of inequalities. Therefore, a dynamic output feedback controller is developed such that 𝐻 and 𝐻 2 performance of the resulting closed-loop system is less than or equal to some prescribed value. Also, 𝐻 and 𝐻 2 performance for a given upperbound of singular perturbation parameter 𝜀 ( 0 , 𝜀 ] are guaranteed. It is shown that the 𝜀 -dependent controller is well defined for any 𝜀 ( 0 , 𝜀 ] and can be reduced to an 𝜀 -independent one so long as 𝜀 is sufficiently small. Finally, numerical simulations are provided to validate the proposed controller. Numerical simulations coincide with the theoretical analysis.