A continuous feedback control approach for real-time scheduling of discrete events is presented in this paper motivated by the need for control theoretic techniques to analyze and design such systems in distributed manufacturing applications. These continuous feedback control systems exhibit highly nonlinear and discontinuous dynamics. Specifically, when the production demand in the manufacturing system exceeds the available resource capacity then the control system "chatters" and exhibits sliding modes. This sliding mode behavior is advantageously used in the scheduling application by allowing the system to visit different schedules within an infinitesimal region near the sliding surface. In this paper, an analytical model is developed to characterize the sliding mode dynamics. This model is then used to design controllers in the sliding mode domain to improve the effectiveness of the control system to "search" for schedules with good performance. Computational results indicate that the continuous feedback control approach can provide near-optimal schedules and that it is computationally efficient compared to existing scheduling techniques.