This thesis aims to develop new control methods for the single-phase quasi-Z-source inverters (qZSIs). The key challenge lies in the design of suitable control method for the qZSI which is a nonlinear multi-input-multi-output (MIMO) system. Hence, from the control point of view, developing an integrated control technique is a challenging issue. Although the conventional control methods attain reasonable responses, suppression of double frequency ripple (DFR), robustness against parameter variations and simplification issues are still open issues. Thus, the proposed new control methods target to achieve these objectives. A novel approach which is created based on the model of the system while tuning the current of the system (MBCC) with DFR mitigation, virtual time constant and active damping to damp the resonances of the LCL filter is presented for a grid-tied qZSI as the first control method in this thesis. The second control method proposed in this thesis is a MIMO sliding mode control (SMC) which aims to control all variables of qZSI concurrently. This control approach not only synchronizes the control of all state variables at the same time, but also offers simplification in the implementation without using proportional-integral (PI) controllers in the dc-side, robustness to parameter variations, DFR mitigation when the sliding constant in the dc-side is selected appropriately and fixed switching frequency by introducing boundary layer technique. The boundary layer smooths the sliding functions and makes them appropriate for the PWMprocess. The applicability of the MIMO SMC method is also investigated for a single-phase high gain Z-source inverter which is called switched Z-source inverter (SZSI) in the literature. The effectiveness and validity of the proposed control methods are supported by simulation results in MATLAB/Simulink environment and the experimental results. The results show that the DFR mitigation approach can remove the DFR in the inductor current successfully and the MBCC method is also an efficient approach with fast dynamic response, zero steady state error and active damping of the resonance. Moreover, MIMO SMC can also achieve the goals with zero steady state error, robustness against parameter variation and fast dynamic response while attaining fixed switching frequency. Keywords: Active damping, double frequency ripple, quasi-Z-source inverter, LCL filter, proportional-resonant control, boundary layer, sliding mode control, switched Z-source inverter