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考虑系统外界干扰、系统参数摄动等非线性扰动环节对中立型时滞系统的H∞影响,提出基于Lyapunov稳定性理论的鲁棒H∞控制器的设计思想。利用线性矩阵不等式(LMI)方法,给出了该类具有状态非线性不确定性中立型时滞系统的鲁棒H∞控制器的设计实例。在非线性不确定函数满足增益有界的条件下,得到了该类时滞系统满足鲁棒H∞性能的一个充分条件。通过求解一个线性矩阵不等式LMI,即可获得鲁棒H∞控制器。仿真结果表明了基于Lyapunov稳定性理论,LMI技术设计的控制器克服了系统外界非线性干扰或系统本身非线性参数摄动的影响,实现了闭环系统的H∞性能条件下的渐近稳定,满足了该系统鲁棒H∞控制的要求。
Considering the influence of nonlinear disturbances such as system external disturbances and system parameter perturbations on the H∞ of neutral time-delay systems, a design idea of robust H∞controller based on Lyapunov stability theory is proposed. A robust H∞ controller design for a class of neutral delay systems with state nonlinearity is given by means of the linear matrix inequality (LMI) method. Under the condition that the nonlinear uncertain function satisfies the boundedness of the gain, a sufficient condition for satisfying the robust H∞ performance of such a time-delay system is obtained. By solving a linear matrix inequality LMI, a robust H∞controller can be obtained. The simulation results show that based on the Lyapunov stability theory, the controller designed by LMI overcomes the nonlinear perturbation of the system or the nonlinear perturbation of the system itself, and achieves the asymptotic stability under the H∞ performance of the closed-loop system. The system robust H∞ control requirements.