The results presented in this paper indicate that the time-optimal control of a multi-variable, time-invariant linear system with inaccessible state variables is made possible by the introduction of a continuous-time observer system. The basic system and the observer system were simulated on a parallel-logic analogue computer for a third-order system and the associated three-dimensional switch surface for the time-optimal control sequence was simulated on a small digital computer: the communications between the analogue and the digital computers were accomplished by a simple interface system