中文摘要：

通过构造参数依赖Lyapunov函数,研究了线性离散不确定系统的广义l2 （ Gl2 ）性能分析问题. 所考虑的线性时不变系统参数不确定性具有凸多面体不确定性形式,同时受外部扰动影响.通过引入自由权矩阵和采用线性矩阵不等式技术,给出了保证系统Gl2 性能的三个充分性判别条件. 通过理论分析,所得结果较已有文献具有更少的保守性. 最后,数值算例验证了此方法的可行性和有效性.

英文摘要：

By constructing the parameter-dependent Lyapunov functions, the generalized l2 （ Gl2 ） perform-ance analysis problem was studied for linear discrete-time uncertain system. The considered linear uncer-tain time-invariant systems are subject to convex polytopic uncertainty. Moreover, the external disturb-ances exist in the system model. By introducing some free weight matrices and using the linear matrix ine-quality technique, three sufficient conditions were proposed to ensure the desired Gl2 performance. It is shown that the proposed results are less conservative than the existing results. Finally, a numerical exam-ple verifies the feasibility and usefulness of the proposed methods.