一类非理想切换系统的H∞控制器设计

针对实际物理过程中普遍存在的动力学切换现象,提出一类具有平滑切换过程的非理想切换系统模型,并研究其鲁棒H_∞切换控制器设计方法.基于平均驻留时间方法与积分不等式理论,得到保证非理想切换系统渐近稳定且满足给定L₂增益的充分条件.在此基础上,以线性矩阵不等式形式给出H_∞切换控制器的设计准则.所提非理想切换系统较之理想切换系统更具一般性,故所得控制方法同样适用于理想切换系统.变体飞行器跟踪控制的应用实例表明,基于设计方法得到的控制器在保证系统稳定性与跟踪性能的同时,对系统参数摄动具有较强的鲁棒性.

H∞ controller design for a class of nonideal switched systems

A class of smoothly switched system model was proposed to describe the phenomena of dynamics switching that generally occured in real-world processes, and the problem of robust H_∞ switching controller design was investigated for systems of this kind. Based on the average dwell time method and the differential inequality theory, the sufficient condition was presented such that asymptotic stability and some given L₂ gain are guaranteed for the smoothly switched system. The design criterion of the robust H_∞ switching controller was further obtained in terms of linear matrix inequalities. The smoothly switched system model covers the prevailing switched system model as a special case; therefore the controller synthesis method in this note is applicable to traditional switched systems. A design example on a morphing aircraft illustrates that the resultant tracking control system qualifies well robustness against parameter uncertainties while possessing stability and acceptable tracking performance.