Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 361640, 21 pages
http://dx.doi.org/10.1155/2011/361640
Research Article

Less Conservative ℋ ∞ Fuzzy Control for Discrete-Time Takagi-Sugeno Systems

Leonardo Amaral Mozelli1 and Reinaldo Martinez Palhares2

1Federal University of São João del-Rei, Campus Alto Paraopeba, Rodovia MG 443 Km 7, 36420 Ouro Branco, MG, Brazil
2Department of Electronics Engineering, Federal University of Minas Gerais, Avenida Antônio Carlos 6627, 31270-010 Belo Horizonte, MG, Brazil

Received 23 August 2010; Accepted 24 January 2011

Academic Editor: Geraldo Silva

Copyright © 2011 Leonardo Amaral Mozelli and Reinaldo Martinez Palhares. 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

New analysis and control design conditions of discrete-time fuzzy systems are proposed. Using fuzzy Lyapunov's functions and introducing slack variables, less conservative conditions are obtained. The controller guarantees system stabilization and ℋ ∞ performance. Numerical tests and a practical experiment in Chua's circuit are presented to show the effectiveness.