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The single-phase unified power-quality conditioner can be treated as a typical switched linear system due to its typical switching dynamic characteristics. However, because the switched model is difficult for controller design, we first transform it to an equivalent discrete system model (EDSM) in light of the pulsewidth-modulation principle. The EDSM is further transformed to a linear equivalent discrete system model (LEDSM) by states reconstruction and linearization at some neighborhood of the equilibrium manifold. The LEDSM, where the pulsewidths are adopted as the controller variables, is a periodical discrete linear system with the constrained control. Since some states cannot be available, the output feedback periodical-switched controller is designed to meet suboptimal performance and stabilize the closed-loop system. Compared with the proportional-integral controller, the output feedback control strategy features better characteristics. The voltage reference for the series inverter is obtained by using an adaptive voltage detection method. Simultaneously based on the detected phase of the system voltage, the instantaneous reactive power theory is adopted to calculate the reference current for the shunt inverter. Additionally, the power flow and power consumption are described and analyzed. Simulation results demonstrate the effectiveness and reliability of the proposed control strategy.