A discrete-time lattice hydrodynamic model with time-delay and delay-independent traffic flux control signal is introduced. The new model is analyzed with the discrete-time Lyapunov stability theorem and a sufficient stable condition of the model is presented in the form of linear matrix inequality. Through numerical simulation, the traffic flow evolution rules under different conditions of time-delay and control gain are demonstrated and compared. All the results show that the traffic system with time-delay can easily evolve into traffic congestion comparing to the traffic system without time-delay. Also the discrete-time traffic flux control signal can improve the stable level of traffic flow.

引入了具有时滞和时滞无关的交通流量控制信号的离散时间网格水动力模型。利用离散时间Lyapunov稳定性定理对新模型进行了分析，并以线性矩阵不等式的形式给出了模型的充分稳定条件。通过数值模拟，证明并比较了不同时延和控制增益条件下的交通流演变规律。所有结果表明，与没有时间延迟的交通系统相比，具有时间延迟的交通系统很容易演变为交通拥堵。离散时间交通流量控制信号也可以提高交通流量的稳定水平。