Research Papers

Asymptotical Synchronization of Lur'e Systems Using Network Reliable Control

[+] Author and Article Information
R. Rakkiyappan

Department of Mathematics,
Bharathiar University,
Coimbatore, Tamil Nadu 641 046, India
e-mail: rakkigru@gmail.com

S. Lakshmanan

Center for Intelligent Systems Research,
Deakin University,
Waurn Ponds, Victoria 3216, Australia
e-mail: lakshm85@gmail.com

C. P. Lim

Center for Intelligent Systems Research,
Deakin University,
Waurn Ponds, Victoria 3216, Australia
e-mail: chee.lim@deakin.edu.au

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 15, 2015; final manuscript received July 24, 2016; published online September 22, 2016. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 139(1), 011004 (Sep 22, 2016) (11 pages) Paper No: DS-15-1273; doi: 10.1115/1.4034368 History: Received June 15, 2015; Revised July 24, 2016

This paper presents the synchronization criteria for two identical delayed chaotic Lur'e systems. Here, we employ network reliable feedback control for achieving synchronization between our considered systems. The advantage of the employed controller lies in the fact that it even works in the case of actuator or sensor failures, which may occur in many real-world situations. By introducing an improved Lyapunov–Krasovskii (L–K) functional and by using reciprocally convex technique, sufficient conditions are given in the form of linear matrix inequalities (LMIs) to ensure asymptotic stability of resulting synchronization error system. Numerical simulations of neural networks and Chua's circuit system are given to verify the effectiveness and less conservatism of the presented theoretical results.

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Grahic Jump Location
Fig. 1

(a) and (b) State response of x(t) and y(t), and (c) state response of r(t)

Grahic Jump Location
Fig. 2

Chaotic attractors of Chua's circuit system

Grahic Jump Location
Fig. 3

State response of x(t) and y(t) in Example 2

Grahic Jump Location
Fig. 4

State response of errors r(t) in Example 2

Grahic Jump Location
Fig. 5

State response of errors r(t) in Example 2 for usual sampled-data control with actuator failure cases

Grahic Jump Location
Fig. 6

State response of errors r(t) in Example 3

Grahic Jump Location
Fig. 7

State response of errors r(t) in system (18) with disturbance ω(t)= sin(t)/[0.1(1+t)]




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