一类不确定时滞系统的时滞依赖型鲁棒H_∞控制器设计新方法  

Robust H_∞ Controller Design for a Class of Linear Systems with Time-varying Delayed State: an Improved LMI Approach

作　　者：夏红伟[1] 马广程[1] 王常虹[1] 

机构地区：[1]哈尔滨工业大学航天学院,黑龙江哈尔滨150001

出　　处：《航空学报》2007年第B08期131-135,共5页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(60504008)

摘　　要：针对一类具有状态滞后和凸多面体不确定性的连续时间系统,研究了其鲁棒H∞控制器的设计问题。通过引入两个附加的松弛矩阵使Lyapunov矩阵和系统矩阵得到分离,得到了一个新的具有更低保守性的鲁棒H∞性能判据,并基于该判据设计了系统的鲁棒H∞状态反馈控制器。设计的状态反馈控制器不但保证闭环系统的二次稳定性,同时使系统的H∞范数小于一个给定的衰减水平γ。并且设计了一个迭代算法来得到问题的次最优解。通过数值仿真验证了所提出的控制器设计方法的可行性和有效性。The problem of robust H∞ controller design for linear systems with parameter uncertainty residing in a polytopic and time-varying delays in states is considered. A new improved LMI representation of H∞ performance is presented for the linear systems with time-varying state delay. The state feedback H∞ controller guarantees not only the quadratic stability of the closed-loop system but also the H∞ norm bound within a γ. The newly proposed criterion exhibits a kind of separation between the system matrices and the positive definite Lyapunov matrices. So the vertex-dependent Lyapunov functions can be adopted, and thus a less conservative result is expected to be obtained. To further refine the suboptimal controller, an iterative algorithm is developed. A numerical example is employed to illustrate the effect of the proposed approach.

关 键 词：自动控制技术 鲁棒控制 参数依赖 状态滞后系统 凸多面体不确定性 

分 类 号：V249.12[航空宇航科学与技术—飞行器设计] TP13[自动化与计算机技术—控制理论与控制工程]