Pole Assignment and LMI Appeoach for Uncertain Switched Systems

研究了一类不确定线性切换系统基干状态反馈的援点配置和LMI方法问题。此类切换系统不仅具有未知但有界的结构不确定性,而且具有外部扰动。利用公共Lyapunov函数,得到一稳定切换控制策略来保证:(1)备线性子系统的特征值位于左半复平面的选定圆内,(2)最小化闭环切换系统的扰动衰减水平。在各子系统不稳定的前提下,设计切换系统的状态反馈控制器,使得在任意切换策略下系统的闭环极点配置在左半复平面,且具有良好的扰动衰减水平,系统渐近稳定。得到了切换系统可状态反馈镇定的充分条件,然后用易于求解的线性矩阵不等式形式表示出结果;最后通过仿真验证所设计的切换系统在状态反馈控制器下渐近稳定,且具有良好的投点配置和最小γ衰减水平。The problem of stale feedback control of continuous-lime switched linear systems with uncertain items is addressed in this paper. Uncertain switched systems' pole assignment and disturbance attenuation level arc sludied. The switched systems not only have unknown, norm-bounded uncertainty in system' s structure, but also have exogenous disturbance. By using common Lyapunov function method, the state feedback robust controllers under arbitrary switching strategy are designed to assure each subsystem's eigenvalue inside a chosen circle on the open left-half complex plane and the stales of the systems asymptotically stable. Then the minimum disturbance attenuation level on Lyapunov function for switched systems is obtained. Both of the pole assignment and minimum disturbance attenuation level of switched systems are obtained. All of these based on convex combinations technique and linear matrix inequalities method, the result is expressed in the form of linear matrix inequalities,which can be solved easily. Finally the simulation shows that the designed controller can make the states of the switched systems asymptotically stable under the arbitrary switching strategy with poles inside chosen circles and minimum disturbance attenuation level.福建省青年科技人才创新项目基金(2005J006);; 厦门大学985二期信息创新平台项