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The chapter 4 describes the dead-beat control laws, for damping the input filter capacitor voltage of a power inverter feeding an electrical motor, but also for limiting the power supply current. The algebraic calculation of the control current uses the transition matrix eigenvalues of the filter discrete-time state-space equation. It takes account of filter parameters, of capacitor voltage and line current measures, of voltage and current set-points, and of voltage and current limits. According to the system input variable number with respect to the number of variables to be controlled, an hybrid control is proposed. The filter control dynamics is shown and discussed as a function of the filter disturbance modes.