Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 734340, 10 pages
Research Article

Stability Analysis of Interconnected Fuzzy Systems Using the Fuzzy Lyapunov Method

1Department of Construction Science and Technology, De-Lin Institute of Technology, No.1, Lane 380, Qingyun Rd., Tucheng, Taipei 236, Taiwan
2Department of Logistics Management, Shu-Te University, 59 Hun Shan Road, Yen Chau, Kaohsiung 82445, Taiwan

Received 10 August 2009; Accepted 4 November 2009

Academic Editor: Carlo Cattani

Copyright © 2010 Ken Yeh and Cheng-Wu Chen. 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.


The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist of J interconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Some stability conditions are derived through the use of fuzzy Lyapunov functions to ensure that the interconnected fuzzy systems are asymptotically stable. Common solutions can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Finally, simulations are performed in order to verify the effectiveness of the proposed stability conditions in this paper.