Z and quasi-Z-source inverters (Z/qZSI) have a nonlinear impedance network on their $dc$ side, which allows the system to behave as a buck–boost converter in their outputs. The challenges derived from the qZSI topology include (a) the control of the voltage and current on its nonlinear impedance network, (b) the dynamic coupling between the $ac$ and $dc$ variables, and (c) the fact that a unique set of switches are used to manage the power at $dc$ and $ac$ side of the system. In this work, a control scheme that combines a PWM linear control strategy and a strategy based on finite control state model predictive control (FCS-MPC) is proposed. The linear approach works during steady state, while the FCS-MPC works during transient states, either in the start-up of the converter or during sudden reference changes. This work aims to show that the performance of this control proposal retains the best characteristics of both schemes, which allows it to achieve high-quality waveforms and error-free steady state, as well as a quick dynamic response during transients. The feasibility of the proposal is validated through experimental results.