不确定时延网络控制系统的稳定性设计

摘要

Since the control systems have characteristics of network time⁃delay and uncertainty in the network environment, a common mode feedback controller without assigning specify parameters in advance is used to establish the closed⁃loop network control system model with the state feedback by taking into account of fact that the lower bound of the maximum allowable net⁃work induced delay is not zero and the system has uncertainty characteristics. The quadratic integral item in Lyapunov⁃Krsaso⁃vskii functional is defined directly by introducing the integral inequality approach,which can avoid the conservative property caused by model transformation of the system and definition of the cross terms. On this basis,the condition that makes the net⁃worked control system robust stability is derived. The state response curve of the system is obtained by conducting Matlab simulation for the model. The system state tends to be stable,which shows the validity and feasibility of the conclusion.%针对网络环境下的控制系统所具有的网络时延和不确定性特点，考虑最大允许网络诱导时延下界不为零及系统带有不确定性的情况，采用不需事先指定参数的更具一般性的状态反馈控制器，建立状态反馈的闭环网络控制系统模型。通过引入积分不等式方法，对Lyapunov⁃Krsasovskii泛函中的二次型积分项直接进行界定，避免了对系统进行模型变换和对交叉项的界定所带来的保守性。在此基础上，推导出使网络控制系统鲁棒稳定的条件。最后通过对模型进行Matlab仿真，得到状态响应曲线。系统状态很快趋于稳定，表明该结论的有效性和可行性。