$H_\infty$ Synchronization for Uncertain Time-Delay Chaotic Systems With One-Sided Lipschitz Nonlinearity

This paper addresses $H_\infty $ synchronization for uncertain chaotic systems with one-sided Lipschitz nonlinearity under the output and intrinsic state delays. By utilizing the one-sided Lipschitz condition and quadratic inner boundedness, constructing an appropriate Lyapunov–Krasovskii (LKF), robust controller design conditions based on Lyapunov stability theory are derived for synchronization of chaotic systems under disturbances or perturbations bounded by $L_{2}$ norm. By introducing the delay-derivative limits and delay-interval bounds into LKF, the intrinsic state time-varying delay can be tackled by the delay-range-dependent strategy. Less conservative stability condition can be obtained by the further improved inequality of Jensen inequality and reciprocally convex approach, which can lead to the tighter upper bound for integral inequality. Numerical simulations are provided to verify the validity of the proposed methodology for synchronization of chaotic systems.