Stability analysis of predictive control systems

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 is , 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.