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针对网络控制系统中时延不确定因素,将时延的不确定性转换为系统状态方程系数矩阵的不确定性,基于LMI和Lyapunov理论,研究了一类具有时延的网络控制系统的稳定性问题,并运用Lyapunov方法和线性矩阵不等式对不确定时延系统进行了稳定性分析。并以Riccati不等式和线性矩阵不等式的形式给出了系统稳定的充分条件,使得在不确定时延情况下,系统达到理想稳定性。最后,通过Matlab工具箱对数值结果进行仿真,在时延相关情况下,求得系统达到闭环稳定时最大允许的时延,表明了设计方法的有效性。
Aiming at the uncertainty of delay in networked control system, the uncertainty of delay is transformed into the uncertainty of coefficient matrix of system state equation. Based on LMI and Lyapunov theory, the stability of a kind of networked control system with time delay is studied. The stability analysis of uncertain time-delay system is carried out by using Lyapunov method and linear matrix inequality. The sufficient conditions for the system stability are given in the form of Riccati inequality and linear matrix inequality so that the system achieves the ideal stability under the condition of uncertain delay. Finally, numerical results are simulated by Matlab toolbox, and the maximum allowable delay when the system reaches closed-loop stability is obtained under the condition of delay, which shows the effectiveness of the design method.