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Delay-range-dependent synchronization of drive and response systems under input delay and saturation

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  • Rehan, Muhammad
  • Tufail, Muhammad
  • Hong, Keum-Shik

Abstract

This paper addresses the synchronization of nonlinear drive and response systems under input saturation and subject to input time-delay. In considering generalized forms of the systems, their dynamics are assumed to satisfy the one-sided Lipschitz condition along with the quadratic inner-boundedness rather than the conventional Lipschitz condition. Further, the time-delays are handled by application of the delay-range-dependent methodology, rather than the delay-dependent one, utilizable for both short and long time-delays. Synchronization controller designs are provided by application of the Lyapunov–Krasovskii functional, local sector condition, generalized Lipschitz continuity, quadratic inner-boundedness criterion and Jensen's inequality. To the best of the authors’ knowledge, a delay-range-dependent synchronization control approach for the one-sided Lipscitz nonlinear systems under input delay and saturation constraints is studied for the first time. A convex-routine-based solution to the controller gain formulation by application of recursive nonlinear optimization using cone complementary linearization is also provided. The proposed methodology is validated for synchronization of modified Chua's circuits under disturbances by considering the input delay and saturation constraints.

Suggested Citation

  • Rehan, Muhammad & Tufail, Muhammad & Hong, Keum-Shik, 2016. "Delay-range-dependent synchronization of drive and response systems under input delay and saturation," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 197-207.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:197-207
    DOI: 10.1016/j.chaos.2016.04.001
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    References listed on IDEAS

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    1. Zhaoxia Peng & Guoguang Wen & Ahmed Rahmani & Yongguang Yu, 2015. "Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(8), pages 1447-1457, June.
    2. Sohaira Ahmad & Raafia Majeed & Keum-Shik Hong & Muhammad Rehan, 2015. "Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, March.
    3. Singh, Piyush Pratap & Singh, Jay Prakash & Roy, B.K., 2014. "Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 31-39.
    4. Fang Liu & Qiang Song & Jinde Cao & Jianquan Lu, 2014. "Pinning Synchronization of One-Sided Lipschitz Complex Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, April.
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