Stability Analysis for Single-Lane Traffic with a Relay Controller in a Closed Loop

Rule-based relay controllers are common in single-lane urban traffic control systems and introduce significant nonlinearity. In this paper, we analyze the closed-loop stability for a traffic process with a relay controller and negative feedback, with respect to several time delays present in the plant. First, we derive models for the road segment and the controller. Second, we investigate the system stability based on describing the function analysis. Finally, we present the numerical results.