带有丢包的线性参数变化系统的H∞控制

摘要

主要研究了一类带有Lipschitz非线性和随机通信丢包的线性参数变化系统(LPV)基于观测器的H∞控制问题.针对信号传递中的随机丢包,使用了已知条件概率分布的Bernoulli分布序列来描述.在随机丢包存在的情况下,利用李雅普诺夫稳定性定理得到了基于观测器的反馈控制器存在的充分条件,使得闭环网络LPV系统不仅是均方指数稳定的,而且满足预定的H∞扰动抑制性能指标;然后利用近似基函数和网格技术将无限维的线性矩阵不等式组的求解问题近似为有限维线性矩阵不等式组的求解问题,提出了一种线性矩阵不等式的方法,设计出了相应的H∞控制器.最后,通过数值仿真验证了所提方法的有效性.%This paper investigates the observer-based H∞control problem of Linear Parameter-Varying(LPV)systems with global Lipschitz nonlinearities and random communication packet losses. In this paper, the random packet loss is modeled as a Bernoulli distributed white sequence with a known conditional probability distribution.Based on Lyapunov stability theory,sufficient conditions for the existence of an observer-based feedback controller are derived in the presence of random packet losses, such that the closed-loop networked LPV system is exponentially stable in the mean-square sense,and a prescribed H∞disturbance-rejection-attenuation performance is also achieved.Then the approximate basis function and the grid technique are used to make the problem of solving an infinite-dimensional linear matrix inequalities be approximated as a finite-dimensional linear matrix inequalities.Then a Linear Matrix Inequality(LMI)approach for designing such an observer-based H∞controller is proposed.Finally,the effectiveness of the proposed method is verified by numerical simulation.