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主要研究一类同时具有时变状态时滞和控制时滞不确定线性系统的鲁棒H∞控制。通过构造带有时滞上下界信息的Lyapunov-Krasovskii函数,在估计其导数上界时把时变时滞和它的上下界之间的关系考虑进去,结合一种由引入自由权矩阵的Park不等式导出了新的二次型积分不等式的方法,得到了一类自治系统的时滞依赖条件并在此基础上设计了H∞控制器。最后用数值算例表明了该时滞系统与状态反馈律所组成的闭环系统具有较好的H∞性能和较低的保守性。
The main research is on a class of robust H∞controls for a class of linear systems with both time-varying state delay and control delay. By constructing the Lyapunov-Krasovskii function with delay upper and lower bound information, the time-varying delay and its upper and lower bounds are taken into account in the estimation of the upper bound of derivatives. A Park inequality introduced by the free-weights matrix is derived A new quadratic integral inequality method is proposed and the delay-dependent conditions for a class of autonomous systems are obtained. Based on this, a H∞controller is designed. Finally, a numerical example is given to show that the closed-loop system composed of the time-delay system and the state feedback law has better H∞ performance and lower conservativeness.