The traffic-responsive signalization problem for an oversaturated intersection is addressed. A new model for intersection called positive switched system is presented. Then, based on the dissipativity analysis results for positive switched system, an online state-feedback strategy for traffic signal in four-phase intersection is proposed. By molding the intersection as a discrete-time switched system, a set of state-feedback controllers is proposed and the green time of each phase in signalization is determined. Finally, a simulation study in comparison with the classic models(bang-bang control) is presented. Simulation result shows the effectiveness of state-feedback control in relieving the oversaturated situation for an intersection.