一类多时延网络控制系统的稳定性分析和鲁棒 H∞控制

摘要

针对一类具有外加扰动的多时延网络控制系统（NCSs），讨论了其稳定性条件和鲁棒H∞控制器设计问题。将采样率、网络诱导时延和丢包转化成系统的时变状态时延，建立系统在连续时域里的多输入多输出（MIMO）数学模型；再利用Lyapunov稳定性定理和自由权矩阵的方法，通过求解若干线性矩阵不等式（LMI），得到该网络控制系统的最大允许时滞上界（MADB）和稳定性条件，然后利用这一条件和非线性最小化方法，导出基于迭代算法的鲁棒H∞状态反馈控制器的设计方法；最后，通过小车倒立摆系统对所推导的稳定性条件和鲁棒H∞控制器设计方法进行了仿真验证，结果表明该方法有效。%Stability analysis and robust H∞control of a class of networked control systems with external disturb-ance and multiple time-delay are addressed.First,a continuous MIMO model was obtained by translating sam-pling rate,network-induced delays and data dropout into time-varying state delays through equipollent deduc-tion.By Lyapunov stability theory and free-weighting matrix approach,and by solving some linear matrix ine-quality,Maximum Allowable Delay Bound (MADB)and the stability condition of NCSs were obtained,and then the design method of robust H∞ controller based on iterative algorithm by considering this condition and nonlinear minimization method.Finally,with inverted pendulum as example,the simulation shows the criterion about the NCS.