On stabilization of unstable second-order systems

The paper is concerned with stabilizing an unstable second-order system by using some of its parameters, periodic with zero mean vibrations. The necessary and sufficient conditions are obtained for the method to be effective. Optimal parameters are obtained for vibrational movements insuring the fastest decay of solutions to the stabilized system. An example is considered which illustrates the application of results to an ionization thermal instability in a $CO_2$ laser.