I. Karafyllis and M. Papageorgiou, "Stability results for simple traffic models under PI-regulator control," IMA Journal of Mathematical Control and Information, vol. 33, no.2, pp. 209-229, Jun. 2016. doi: 10.1093/imamci/dnu040
https://doi.org/10.1093/imamci/dnu040
This paper provides necessary conditions and sufficient conditions for the (global) input-to-state stability property of simple uncertain vehicular-traffic network models under the effect of a PI regulator. Local stability properties for vehicular-traffic networks under the effect of PI regulator control are studied as well: the region of attraction of a locally exponentially stable equilibrium point is estimated by means of Lyapunov functions. All obtained results are illustrated by means of simple examples.