The use of a low-order model to determine the approximate time-optimal switching function for a given plant has been experimentally investigated. This paper utilizes Liapunov's second method to determine asymptotic stability in the large or, in some cases, boundedness of the states of these predictive or quasi-time-optimal control systems. The basic model transfer function isK/s (Ts+1) (K, T > 0), since previous results indicated its versatility for controlling plants of various forms. Plants considered are second-order, both linear and nonlinear, and higher order linear plants. Results show that systems with stable, controllable second-order plants will be asymptotically stable in the large, and systems with linear controllable high-order plants with no more than two free integrations will have ultimately bounded error and error rate. Examples are presented to illustrate the results.