一类具有两个区间状态时变时滞的广义离散系统的新的有界实引理

New bounded real lemma for a class of singular discrete-time systems with two interval time-varying delays in state

针对一类具有两个区间状态时变时滞的广义离散系统,通过构造合适的李雅普诺夫函数,结合线性矩阵不等式放缩技术和时滞划分技术,得到一个新的有界实引理,从理论上将该有界实引理和一个现有结论进行了比较,结果表明,改进李雅普诺夫函数后的有界实引理比文献中的有界实引理具有更小的保守性。数值实验结果表明,当两个时滞区间上下界取值固定时,如果不对时滞区间进行划分,改进后的有界实引理和文献中的有界实引理算得的H∞性能指标是相同的;当对时滞区间划分后,利用新的方法获得的H∞性能指标小于文献中的值,而且随着时滞区间划分份数的增多,H∞性能指标会进一步减小。实例表明,本方法优于文献中已有的方法。

For a class of discrete singular systems with two interval time-varying delays in state, a new bounded real lemma is given with the linear matrix inequalities scaling techniques and delay partition technology by constructing appropriate Lyapunov functions. The proposed bounded real lemma is compared with an existing conclusion theoretically and the results show that the proposed bounded real lemma is less conservative. A numerical experiment is carried out to verify that the proposed method is superior and effective. When the bounds of two interval time-varying delays are fixed, the results of a numerical example shows that （i） if delay interval is not divided, H∞ performance index obtained by the new meth- od is the same as that by the bounded real lemma in literature; and （ii） when the time delay interval is divided, the H∞ performance index with the new way is less than that with the bounded real lemma in the literature. Furthermore, with increasing number of the delay interval division, the H∞ performance index decreases. All the results mean that the new method is better than one in the literature mentioned.