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针对一类状态和输入同时具有时滞的不确定离散时滞奇异系统,研究了该类系统的弹性H∞控制器的设计问题,其中不确定性存在于系统的状态矩阵和输入矩阵当中,且满足范数有界条件。利用Lyapunov函数理论,以线性矩阵不等式(LMI)形式给出了系统弹性H∞控制器存在的充分条件及设计方法,所设计的H∞控制器既保证了闭环系统对所有允许的不确定性,又能保证系统具有一定的H∞性能γ。最后,通过数值算例说明该方法的实效性。
For a class of uncertain discrete-time singular systems with time delay and input delay, this paper studies the design of elastic H∞ controllers of this kind of system, in which the uncertainty exists in the state matrix and the input matrix of the system Meet the norm bounded conditions. By using Lyapunov function theory, sufficient conditions and design method for the existence of the system elastic H∞ controller are given in the form of linear matrix inequalities (LMI). The designed H∞ controller not only guarantees all possible uncertainties of the closed-loop system, But also ensure that the system has a certain H∞ performance γ. Finally, a numerical example is given to illustrate the effectiveness of this method.