考虑随机时滞的非线性网控系统鲁棒L2–L∞控制

摘要

本文考虑了由Takagi-Sugeno(T-S)模糊模型描述的一类连续非线性网络控制系统基于观测器的鲁棒L2-L∞控制器设计问题.假设网络环境下存在的时变时滞具有特定的随机特性,通过引入一个伯努利随机变量表示时滞在不同区间上分布的概率,建立一个新的具有概率分布信息的系统模型.根据平行分布补偿法(parallel distribu-tion compensation,PDC)和Lyapunov稳定性理论,建立基于T-S模糊模型的使系统均方指数稳定且满足L2-L∞的性能判据.并利用线性矩阵不等式(linear matrix inequality,LMI)技术同时得到状态观测器增益矩阵和控制器增益矩阵.最后,仿真结果验证了该方法的有效性.%In this paper, the problem of observer-based robust L2-L∞ controller design for a class of continuous non-linear networked control systems is considered in Takagi-Sugeno (T- S) fuzzy model. A new system model with probability distribution information is established by introducing a Bernoulli random variable to represent the probability of the delay distribution in different intervals, assuming that the time-varying delay in the network environment has a certain stochastic property. According to the parallel distributed compensation (PDC) and Lyapunov stability theory, the L2-L∞ criterion based on T- S fuzzy model is established to make the system mean square exponential stability. And the state observer gain and the controller gain matrixes are obtained by linear matrix inequality (LMI) technique. Finally, the simulation results verify the effectiveness of the proposed method.