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Combination–combination synchronisation; time-delay chaotic systems; adaptive control; Lyapunov– Krasovskii functional theory

In this article, an adaptive control method is proposed to study the combination–combination synchronisation phenomenon of four non-identical time-delayed chaotic systems for fully unknown parameters with parametric uncertainties and external disturbances. Based on the Lyapunov–Krasovskii functional theory, an appropriate adaptive controller is constructed so that a globally and asymptotically stable synchronisation state can be established between the master and the slave systems. Unknown parameters are identified by designing suitable parameter update laws. To elaborate the presented scheme, double-delay Rossler and time-delay Chen systems are considered as the master systems and time-delay Shimizu–Morioka and time-delay modified Lorenz systems are considered as the slave systems. Numerical simulations are presented to justify the theoretical analysis.

AYUB KHAN¹ MRIDULA BUDHRAJA² AYSHA IBRAHEEM³

1. Department of Mathematics, Jamia Millia Islamia, Delhi 110 025, India
2. Department of Mathematics, Shivaji College, Delhi 110 027, India
3. Department of Mathematics, University of Delhi, Delhi 110 007, India

Published

1 August 2018

Manuscript received

25 August 2017

Manuscript revised

24 December 2017

Accepted

10 January 2018

Early published

Unedited version published online

Final version published online

26 June 2018