Discrete time sliding mode approach to synchronization of modulated two-phase harmonic oscillator

This paper explores two-phase harmonic oscillator synchronization with a referent oscillator, whose amplitude and phase are modulated by two arbitrary smooth functions, respectively. Synchronization between modulated referent and controlled oscillator is based on amplitude and phase control, and pursued by employing a discrete time variable structure control system. Synchronization is achieved by organizing a quasi-sliding mode along intersection of two appropriate nonlinear sliding surfaces. Discrete-time variable structure controllers are proposed, which provides the desired motion. Mathematical analysis as well as experimental results are presented.