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研究了一类参数不确定的具有多个时滞的Lur’e型控制系统与时滞相关绝对稳定性问题.通过将原系统变换为等价的奇异系统,利用Moon不等式放大向量积,构造出一个新的Lya-punov-Krasovskii泛函.并由此基于线性矩阵不等式,得到了系统与时滞相关绝对稳定的充分条件.这些充分条件无须预调任何参数矩阵,可以直接运用Matlab软件中LMI工具箱求解.数值例子表明,与现有结果相比,本文结果较大地改进了保证不确定时滞Lur’e型控制系统绝对稳定的时滞界.
A class of uncertain Lur’e-type control systems with uncertain parameters and delay-dependent absolute stability problems are studied. By transforming the original system to an equivalent singular system and using Moon inequality to enlarge the vector product, A new Lya-punov-Krasovskii functional is obtained. Based on the linear matrix inequality, the sufficient conditions for the absolute stability of the system to delay are obtained. Without any parameter matrix preconditioning, the LMI tool in Matlab software The numerical example shows that compared with the existing results, the results in this paper greatly improve the absolute stability of the Lur’e-type control system with uncertainties.