一类不确定广义周期时变系统的鲁棒H_∞控制

ROBUST H_∞ CONTROL FOR A CLASS OF LINEAR TIME-VARYING UNCERTAIN PERIODIC GENERALIZED SYSTEMS

本文研究了状态矩阵具不确定性广义周期时变系统的鲁棒H∞控制问题.利用线性矩阵不等式(LMI)方法,在给出不确定广义周期时变系统广义可镇定和广义二次可镇定且具有H∞性能指标概念的基础上,得到了该系统广义二次可镇定且具有H∞性能指标γ的充要条件,并给出了相应的鲁棒H∞状态反馈控制律的设计方法,推广了周期系统的鲁棒控制理论结果.最后,通过数值算例说明了设计方法的有效性.

This paper considers the problem of robust H∞ control for linear time-varying periodic generalized systems with uncertainty in the state matrix.The necessary and sufficient conditions for generalized quadratic stabilization with a H∞ performance index γ are put forward and the corresponding robust H∞ state feedback control law is proposed by using the method of LMI on basis of the concepts of generalized stabilizability and generalized quadratic stabilizability with H∞ performance index for uncertain periodic generalized systems,so that the robust control theories of periodic generalized systems are generalized.Finally,a numerical example is given to illustrate the effectiveness of the approach.