多时滞广义离散系统的H_∞性能分析

H_∞ analysis for descriptor discrete systems with multi-time delay

讨论了带有多时滞的广义离散系统的H∞性能问题.利用线性矩阵不等式,证明了该系统具有广义γ-次优H∞性能的一个充分条件是存在对称可逆矩阵P和对称正定矩阵Si(i=1,…,N)满足相关条件,并将广义离散系统的有界实引理推广到多时滞广义离散系统的情形,证明了相应常规系统具有γ-次优H∞性能的一个充分条件是存在对称正定矩阵P和对称正定矩阵Si(i=1,…,N)满足一定条件.通过数值算例验证了结论的有效性.

H∞ analysis for descriptor discrete systems with multi-time delay is considered. By means of linear matrix inequalities, it is proved that a sufficient condition for the system to have the general γ- suboptimal H∞ performance is that there exist a symmetric and invertible matrix P and positive definite matrices Si （ i = 1,…, N） satisfying some conditions. Furthermore, the general bounded real lemma （GBRL） for descriptor discrete systems is extended to the system with multi-time delay. Finally, it is proved that a sufficient condition for the corresponding normal system to have γ- suboptimal H∞ performance is that there exist symmetric and invertible matrix P and positive definite matrices Si （i = 1,…, N ） satisfying certain conditions. And a numerical example is presented to illustrate the efficiency of our results.