双线性奇异摄动系统的无源控制器设计  

Passive Controller Design for Bilinear Singularly Perturbed Systems

作　　者：张秀华[1] 任佳旭 ZHANG Xiuhua;REN Jiaxu(School of Sciences,Northeastern University,Shenyang 110819,China)

机构地区：[1]东北大学理学院,辽宁沈阳110819

出　　处：《沈阳大学学报（自然科学版）》2023年第1期26-32,41,共8页Journal of Shenyang University：Natural Science

基　　金：国家自然科学基金资助项目(61673100)。

摘　　要：研究了1类不确定变时滞双线性奇异摄动系统的无源控制。通过构造依赖于奇异摄动参数ε的Lyapunov函数,采取线性矩阵不等式和范数有界的方法,获得了使系统渐近稳定和严格无源的时滞依赖的充分条件,进而利用线性矩阵不等式的解给出了无源控制器的设计方法。考虑到系统模型的复杂性,给出了时滞独立的充分条件,从而降低了线性矩阵不等式的阶数。提出了一种奇异摄动参数ε允许上界的估计方法。通过数值仿真验证了以上方法的有效性。The passive control of a class of bilinear singularly perturbed systems with uncertainty and time-varying delay was studied. Firstly, by constructing a Lyapunov function dependent on the singular perturbation parameter ε and adopting the methods of linear matrix inequality and norm bounded, delay-dependent sufficient conditions for the asymptotic stability and strict passive of the system were obtained. Then, the design method of passive controller was given by using the solution of linear matrix inequalities. Considering the complexity of the system model, a delay-independent sufficient condition was given, which reduces the order of linear matrix inequality. At the same time, an estimation method of the allowable upper bound of singular perturbation parameter ε was proposed. Finally, the effectiveness of the above methods was verified by numerical simulation.

关 键 词：双线性奇异摄动系统 无源控制 线性矩阵不等式 时滞依赖 时滞独立 奇异摄动参数 变时滞 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]