一类不确定线性时变时滞系统的鲁棒H∞控制

Robust H∞ Controller Design for a Class of Uncertain Linear Systems with Time-varying and Control Delay

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。

Robust Hoocontroller design for a class of uncertain linear delay systems with time-varying and control delay has been studied in this paper, based on Lyapunov stability theory and linear matrix inequality. By constructing a Lyapunov-Krasovskii function based on the upper and lower bound time-delay information, the upper bound of its derivative is estimated considering the relationship between the time-varying delay and its upper and lower bounds, then combining with the new quadratic integral inequality derived by Park inequality which has introduced the freedom matrix to get delay-dependent conditions of a class of autonomous systems,a the robust Hoocontrol law is further designed. Finally, a numerical example is given to illustrate the better performance and less conservativeness of the closed-loop system consisting of delay system and state feedback law.