Integral Input-to-State Stability of Traffic Flow with Variable Speed Limit

Abstract In this paper, a variable speed limit controller is proposed to ensure integral input-to-state stability of the traffic state by using saturated feedback. The ordinary differential equations model of traffic flow is used with a two-phase fundamental diagram to design the controller. A common Lyapunov function is found for both phases which ensures the integral input-to-state stability of the closed-loop system. Proposed controller is tested with numerical examples to show the robustness properties particularly bounded energy frequently bounded state and bounded energy weakly converging state which are the characterizations of the integral input-to-state stability.