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

• Published in: Chaos, solitons and fractals Vol. 87; pp. 197 - 207
• Main Authors: Rehan, Muhammad, Tufail, Muhammad, Hong, Keum-Shik
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2016
• Subjects: Delay-range dependency; Input delay; Input saturation; One-sided Lipschitz condition; Synchronization; One-sided Lipschitz condition; Input saturation; Input delay; Delay-range dependency; Synchronization
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2016.04.001

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.