中文摘要：

基于广义KYP引理,研究了奇异摄动系统的有限频段正实性能.根据奇异摄动系统的双频标特性,即有低频和高频两种频域尺度,应用广义KYP引理,分别研究了奇异摄动系统的降阶子系统在其低频段和高频段的正实性,并以线性矩阵不等式形式给出了上述子系统在有限频段正实的充分必要条件.在此基础上,进一步证明了奇异摄动系统在一定条件下是部分频段正实的.

英文摘要：

The finite positive realness property of singularly perturbed systems is studied based on generalized Kalman-Yakubovic -Popov（KYP） lemma approach.According to the two-frequency scale property of singularly perturbed systems,namely the low（slow） frequency and high（fast） frequency,generalized KYP lemma is applied to the reduced-order subsystems of singularly perturbed systems in the corresponding frequency domain.Then sufficient and necessary conditions are derived to make sure that the subsystems are finite frequency positive realness（FFPR）.Furthermore,it is proved that the singularly perturbed systems are FFPR under certain conditions.