A system is proposed which uses a linear network in the forward path of a second-order on-off control system to achieve time optimum response for step inputs. The system, here referred to as the ‘error-network system’, is compared with several other proposals for various input signals. Among the other proposals is a novel function-generator system which achieves optimum switching for both step and ramp input signals. The error-network system compares well in performance with more complex systems.