This study deals with a general method for the analysis of a semi-active control technique for a fast-shunt switching system. The benefit of the semi-active system is the reduction in power consumption, which is a significant disadvantage of a fully active system compared with a passive system. A semi-active system under consideration is a semi-actively shunted piezoelectric system, which converts the strain energy into electrical energy through strong electromechanical coupling achieved though the piezoelectric phenomenon. Our proposed semi-active approach combines a PZT-based energy harvesting with a fast switching system driven by a Pulse-Width Modulated (PWM) signal. The fast switching system enables continuous adaptation of vibration energy control/harvesting by varying the PWM duty cycle. This contrasts with a conventional capacitance switching system that can only change the capacitance at discrete values. The analysis of the current piezoelectric system combined with a fast-switching system poses a considerable challenge as it contains both continuous and discrete characteristics. The study proposes an enhanced averaging method for analyzing the piecewise linear system. The simulation of the averaged system is much faster than that of the time-varying system. Moreover, the analysis derives error bounds that characterize convergence in the time domain of the averaged system to the original system. The dissertation begins with the derivation of the equations governing the physics of a piezostructure combined with an electrical switching shunt network. The results of the averaging analysis and numerical simulation are presented in order to provide a basis for estimating the structural responses that range between open- and short-circuit conditions which constitutes two limiting conditions. An experimental study demonstrates that the capacitive shunt bimorph piezostructure coupled with a single switch can be adjusted continuously by varying the PWM duty cycle. And the behavior of such hybrid system can be well predicted by the averaging analysis. / Ph. D.