不确定Delta算子切换系统的鲁棒控制研究

Study on Robust Control for Uncertain Switched Systems Using Delta Operator

研究了一类参数不确定线性Delta算子切换系统的鲁棒H∞控制问题。针对传统采用的Delta算子切换系统仅限于多Lyapunov函数方法,使系统仅实现渐进稳定,收敛速度慢。为了提高控制系统的稳定性,解决系统的状态反馈鲁棒H∞控制的难点问题,首次提出利用多Lyapunov函数和平均驻留时间方法,以线性矩阵不等式的形式给出了参数不确定Delta算子切换系统指数稳定性条件,并进行了H∞性能分析,从而进一步给出系统鲁棒H∞控制器的设计方法。所设计的控制器不但保证系统参数不确定时闭环系统指数稳定,而且满足所期望的H∞性能指标。仿真结果证明了设计方法的有效性和可行性。

In this paper,robust H∞ control problems of a class of parameter uncertain switched systems using Delta operator have been studied.Currently,the research on Delta operator switched systems is only based on multiple Lyapunov function theory,and the systems are asymptotic stable.In order to improve the stability and resolve the hard problem of the state feedbake robust H∞ control,an approach based on multiple Lyapunov function theory and average dwell time was presented firstly.A sufficient condition for the existence of stability of the parameter uncertain delta operator switched system was presented in terms of LMI,and the H∞ performance was analyzed.Then,the designing method of robust H∞ controller was proposed.The designed robust H∞ controller can not only guarantee the closed-loop system with uncertain parameter to be asymptotically stable,but also satisfy the expected H∞ performance.A simulation example was given to illustrate the effectiveness and feasibility of the proposed method.