线性多时滞不确定离散时间线性系统的时滞相关H_∞控制

Delay-dependent H-infinity control for linear discrete-time uncertain systems with multiple unknown delays

讨论了线性多时滞不确定离散时间线性系统的时滞相关H_∞控制问题．首先,建立了一个基于二次型项的有限和不等式．然后,利用这一不等式,采用Lyapunov-Krasovskii泛函方法,获得了系统不仅内部稳定而且具有给定的H_∞性能的时滞相关条件,同时以LMI的形式给出了无记忆H_∞控制器的设计方法．最后,数值例子说明了本文方法的有效性．

The delay-dependent H-infinity control of linear discrete-time uncertain systems with unknown delays is discussed via memoryless state feedback. Firstly, an inequality for finite sums of quadratic terms is established. Based on a linear matrix inequality （LMI）, a new delay-dependent condition is then derived by employing Lyapunov-Krasovskii functional method, which can ensure that the resulting closed-loop system is asymptotically stable with a prescribed H-infinity performance. Moreover, the suitable H-infinity controller is designed in light of the feasibility of the obtained LMI. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.