A method is developed, using the quadratic form of canonical uncoupled state variables as a Lyapunov function to determine the switching logic for a quasi-optimum control of a non-linear dynamic system. The system is capable of being extended to any order system and any number of controls, subject to certain practical limitations noted in the analysis. A computational scheme for determining the canonical state variables and control functions is presented and a topological interpretation is made of the choice of variables used for the control logic calculation. The controller based on the method described is applied to a non-linear second-order system. Phase trajectories for both the uncontrolled and controlled systems are obtained by means of a digital computer simulation. Various aspects of the theoretical limitations of the method presented are investigated and the experimental results are analyzed with respect to the theoretical predictions.