This doctoral thesis joins to intensive studies of the power system dynamics and stability in different modes of operation and system states. A new synchronous generator excitation controller based on Lyapunov theory was developed. Control law of the new excitation controller was obtained using a control Lyapunov function. Simulation models for the excitation controller based on Lyapunov theory and the classic PI excitation controller, with and without a power system stabilizer, were developed. Simulation models were used to determine the controller parameters of the excitation control in classic structure, with and without a power system stabilizer, as well as to determine the parameters of the excitation controller based on Lyapunov theory. Algorithms and structures of classic excitation systems, and algorithm and structure of excitation system based on Lyapunov theory were implemented on a digital system cRIO-9014. On the laboratory model (generator 83kVA) experimental responses of the classic excitation system, with and without a power system stabilizer, and excitation system based on Lyapunov theory were recorded. Experimental responses were recorded for step changes of generator reference voltage, step changes of mechanical power, opening and closing a circuit breaker on one of two transmission lines, as well as for three and two phase short circuit faults on one of two transmission lines. Comparing the experimental responses and quality control numerical criteria of the specified excitation systems, the system based on Lyapunov theory has better performance. It widens the generator stability area and is more robust compared to conventional excitation systems. Virtually does not depend on the generator operating point and the power systems state.