具有时延和丢包的网络控制系统的镇定

Stabilization of networked control systems with time-delay and data packet dropout

将包含有界、不确定网络诱导时延和数据包丢失的网络控制系统(NCSs),建模为一类具有时变输入时延的连续时间系统;利用Lyapunov-Krasovskii定理和自由权矩阵法,推导出线性矩阵不等式(LMI)形式的网络控制系统渐近稳定的充分条件;并通过矩阵变换,将NCSs渐近稳定的充分条件转化为LMI形式的状态反馈控制器镇定算法.由于在推导过程中未使用常规的牛顿-莱布尼茨公式,而是通过约束不等式引入自由权矩阵,增加了LMI条件中权矩阵的个数,从而减小了系统的保守性.通过数值仿真验证了算法的有效性,与已有方法相比,在结果的保守性和数学计算的复杂程度上,均有较大幅度改进.

The networked control systems（NCSs） with bounded,uncertain network-induced delay and data packet dropout were modeled as a class of continuous-time systems with time-varying input delay.Based on Lyapunov-Krasovskii theorem and free weighting matrix approach,a sufficient asymptotic stability condition for the NCSs in the form of linear matrix inequality（LMI） was derived.Through matrix transformation,the condition was changed into the LMI-based algorithm for the state feedback controller design.During the derivation,free weighing matrices were introduced through constraint inequality instead of conventional Newton-Leibniz equality,so the number of the LMI＇s weighted matrices was increased and the system conservativeness was reduced.Numerical examples were presented to verify the effectiveness of the proposed algorithm.Both the conservativeness of the results and the complexity of the mathematical calculations were considerably improved in comparison with the existing methods.