Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

Abstract

This article addresses the synchronization of nonlinear master-slave systems under input time-delay and sloperestricted input nonlinearity. The input nonlinearity is transformed into linear time-varying parameters belonging to a known range. Using the linear parameter varying (LPV) approach, applying the information of delay range, using the triple-integral-based Lyapunov-Krasovskii functional and utilizing the bounds on nonlinear dynamics of the nonlinear systems, nonlinear matrix inequalities for designing a simple delay-range-dependent state feedback control for synchronization of the drive and response systems is derived. The proposed controller synthesis condition is transformed into an equivalent but relatively simple criterion that can be solved through a recursive linear matrix inequality based approach by application of cone complementary linearization algorithm. In contrast to the conventional adaptive approaches, the proposed approach is simple in design and implementation and is capable to synchronize nonlinear oscillators under input delays in addition to the slope-restricted nonlinearity. Further, time-delays are treated using an advanced delay-range-dependent approach, which is adequate to synchronize nonlinear systems with either higher or lower delays. Furthermore, the resultant approach is applicable to the input nonlinearity, without using any adaptation law, owing to the utilization of LPV approach. A numerical example is worked out, demonstrating effectiveness of the proposed methodology in synchronization of two chaotic gyro systems.

Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control

“…Jia et al proposed a time-delayed coupled FHN system and studied its stability and Hopf bifurcation 58 . Riaz et al used a nonlinear drive-response system with time-delay and under the effect of slope restricted input nonlinearity to investigate the synchronization phenomenon 64 . Zaheer et al addressed the synchronization in non-linear coupled time-delayed systems by developing a novel state feedback delay-range-dependent control scheme 65 .…”