The paper provides a detailed study of switching conditions of minimum-time control systems based on application in engineering. By analysis in theory and experiment, the authors deduce a set of switching conditions with state and control variabes inequality constraints, the variations of system parameters and the time-delay of computer in real time control. As an example, a DC motor speed control system is considered. By digital simulation and physical experiments,these conditions proved to be correct. The method in this paper is also suitable for other control systems using compound control algorithm.