非线性扰动的关联时滞广义大系统的二次稳定与H_∞控制  

Quadratic Stability and Control for Large-scale Interconnected Time-delay Descriptor Systems with Nonlinear Perturbations

作　　者：闫运平[1] 马跃超[1] 张庆灵[2] 常旭照 

机构地区：[1]燕山大学理学院,河北秦皇岛066004 [2]东北大学系统科学研究所,辽宁沈阳110004 [3]邢台市第六中学,河北邢台054000

出　　处：《四川文理学院学报》2009年第5期17-20,共4页Sichuan University of Arts and Science Journal

基　　金：国家自然科学基金<导数项系数矩阵具有不确定性的广义系统的鲁棒控制>(课题编号:60574011)成果之一

摘　　要：针对非线性扰动的关联时滞广义大系统,研究了其二次稳定性及H∞状态反馈控制器的设计问题。假设其中的不确定性是范数有界的,通过构造改进的Lyapunov泛函,给出了其二次稳定性及H∞状态反馈控制器存在的条件。仅通过求解相应的线性矩阵不等式(linear matrix inequality,LMI)就可得到鲁棒H∞控制器,设计的控制器对所有容许的不确定性不仅使得相应的闭环系统渐进稳定,也能保证闭环系统满足一定的H∞性能指标,达到抑制干扰的效果。最后,用数值算例及仿真验证了所给方法的有效性。This paper focuses on the research of quadratic stabilization and H∞ controller designed for the large -scale interconnected time - delay descriptor systems with nonlinear perturbations. Based on the modified Lyapunov functions, under the assumption that the uncertainty is norm - bounded, existing conditions of quadratic stabilization and state feedback controller are given. The controller can be obtained by solving the corresponding linear matrix inequality. This controller designed can make the closed -loop systems asymptotically stable, as well as satisfying H∞ properties to achieve disturbance attenuation. At last, a numerical example and simulation testing are presented to illustrate the validity of this approach.

关 键 词：非线性扰动 时滞 不确定性 二次稳定 

分 类 号：O29[理学—应用数学]