基于LMI的一类不确定奇异系统的鲁棒控制  

Robust Control of a Uncertain Generalized Systems Based on the LMI

作　　者：王娟[1,2] 张秀华[1] 

机构地区：[1]东北大学系统科学研究所,辽宁沈阳110819 [2]铁岭师范高等专科学校理工学院,辽宁铁岭121000

出　　处：《控制工程》2013年第4期691-693,698,共4页Control Engineering of China

基　　金：国家自然科学基金(61174073)

摘　　要：针对奇异系统、双线性系统、时滞系统和不确定系统四方面结合的复杂系统进行了鲁棒控制研究。基于李雅普诺夫稳定性理论和线性矩阵不等式方法,此外还利用了集合域内放大的方法,对不确定项的参数是时变的但满足范数有界的奇异时滞的双线性系统,推导出其闭环系统鲁棒镇定的充分条件,给出了使得闭环系统鲁棒镇定的状态反馈控制器设计方法。定理基于LMI的方法解决了介于线性和非线性之间的一类不确定时滞奇异双线性系统的鲁棒控制问题,此方法设计的状态反馈控制器更加简单有效,使得系统能快速达到稳定状态。数值仿真说明了定理的合理性和有效性,为解决相关工程控制问题提供了一定理论依据。The problem of robust control for complex systems that combine generalized system, bilinear system and uncertain system with time - delay were studied. Using the theory of Lyapunov stabilization, the sufficient condition of stabilization for SBS with time - delay and uncertainty, where uncertainties are norm - bounded and are varied with the time, is given based on the method of linear ma- trix inequality and using the way of enlargement in the set domain together. Moreover, the designed state feedback controller can make the closed - loop system stable. The related theory for robust control of SBS with uncertain time - delay lying between nonlinear and lin- ear is solved based on LMI . The designed state feedback controller is more simple and more effective, which makes the closed - loop system to reach a steady state more quickly. The effectiveness and rationality of the theory are verified by the numerical example. Thus , the theory provide a certain theoretical basis for engineering control question.

关 键 词：时滞不确定性 奇异系统 鲁棒控制 李亚普诺夫函数 线性矩阵不等式. 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]