## Abstract and Applied Analysis

### Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control

Feng-Hsiag Hsiao

#### Abstract

This study presents an effective approach to realize the optimal ${H}^{\infty }$ exponential synchronization of multiple time-delay chaotic (MTDC) systems. First, a neural network (NN) model is employed to approximate the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov’s direct method to ensure that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Based on the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal ${H}^{\infty }$ performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is provided to illustrate the concepts discussed throughout this work.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 742821, 19 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393450455

Digital Object Identifier
doi:10.1155/2013/742821

Mathematical Reviews number (MathSciNet)
MR3090290

#### Citation

Hsiao, Feng-Hsiag. Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 742821, 19 pages. doi:10.1155/2013/742821. https://projecteuclid.org/euclid.aaa/1393450455

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