Zaheer Muhammad Hamad, Rehan Muhammad, Mustafa Ghulam, Ashraf Muhammad
Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), P. O. Box 45650, Islamabad, Pakistan.
Department of Electronics Engineering, Mohammad Ali Jinnah University, Islamabad, Pakistan.
ISA Trans. 2014 Nov;53(6):1716-30. doi: 10.1016/j.isatra.2014.09.007. Epub 2014 Oct 13.
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies.
本文针对耦合非线性时滞系统中的混沌同步问题，提出了一种新颖的状态反馈延迟范围相关控制方法。两个系统之间的耦合被视为具有时滞的非线性耦合。本研究纳入了固有延迟和耦合延迟的时变特性，以在更广泛的范围内合成质量更高的同步控制器。利用李雅普诺夫 - 克拉索夫斯基（LK）泛函推导延迟范围相关条件，这些条件可通过传统线性矩阵不等式（LMI）工具求解。所得到的主从时滞系统混沌同步控制方法考虑了固有延迟和耦合时滞的非零下界。此外，已将延迟相关同步条件确立为所提出的LK泛函处理的一种特殊情况。此外，还给出了一个与延迟速率无关的延迟范围相关条件，以解决延迟导数上界未知的情况。通过最小化从干扰到同步误差的L2增益，制定了一种鲁棒状态反馈控制方法，用于时滞混沌网络在L2范数有界扰动下的同步。给出了时滞混沌网络的数值仿真结果，以表明所提出的延迟范围相关混沌同步方法的有效性。
