Exponential stability analysis of gammadelayed and gap systems for the traffic flow model in the loop

In this paper, the efficiency of the traffic flow model in the loop is improved by analyzing the exponential stability of delayed systems with gamma distribution and gaps through a new delaydependent regulatory structure. The proposed structure is based on the conversion of a distributed delayed system to a discrete delay system, in which for bothN = ۱ and N > ۱ conditions, sufficient exponential stability conditions of the system are derived by considering the augmented Lyapunov functional function. The proposed delay control with the help of repeated delays causes rapid convergence of states and ensures sufficient conditions of exponential stability. Also, using the Lyapunov function, an additive independent of the exponential stability delay is developed for this type of system, which makes it possible to study the stability of the delayed systems using the Lyapunov functions, and the random stability conditions of the system in the form of matrix inequalities linear is provided. This method hasbeen tested by simulation on the traffic flow model in the loop for both N = ۱ and N > ۱ mode and has been compared with other similar methods.

کلیدواژه ها:

Gamma-delayed ، Gap systems ، Traffic flow ، Exponential stability.