## Journal of Applied Mathematics

### Decentralized Control of Uncertain Fuzzy Large-Scale System with Time Delay and Optimization

#### Abstract

This paper studies the decentralized stabilization problem for an uncertain fuzzy large-scale system with time delays. The considered large-scale system is composed of several T-S fuzzy subsystems. The decentralized parallel distributed compensation (PDC) fuzzy control for each subsystem is designed to stabilize the whole system. Based on Lyapunov criterion, some sufficient conditions are proposed. Moreover, the positive definite matrices ${P}_{i}$ and PDC gain ${K}_{ij}$ can be solved by linear matrix inequality (LMI) toolbox of Matlab. Then, the optimization design method for decentralized control is also considered with respect to a quadratic performance index. Finally, numerical examples are given and compared with those of Zhang et al., 2004 to illustrate the effectiveness and less conservativeness of our method.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 246705, 19 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495089

Digital Object Identifier
doi:10.1155/2012/246705

Mathematical Reviews number (MathSciNet)
MR2904529

Zentralblatt MATH identifier
1244.93085

#### Citation

Zhang, Hang; Wang, Xia; Wang, Yi-Jun; Sun, Zhao-Mei. Decentralized Control of Uncertain Fuzzy Large-Scale System with Time Delay and Optimization. J. Appl. Math. 2012 (2012), Article ID 246705, 19 pages. doi:10.1155/2012/246705. https://projecteuclid.org/euclid.jam/1355495089