The classic model predictive control leads to a variable switching frequency which could produce resonances in the input filter of the matrix converter, affecting the performance of the system. This paper proposes two methods to mitigate the resonance of the input filter in order to solve this issue. The first method consists in a hybrid combination of model predictive current control with instantaneous reactive power minimization and an active damping method which consists in to emulate a virtual resistor in parallel to the input filter's capacitor. The second method imposes a sinusoidal source current instance to minimize the instantaneous reactive power at the input side. Both methods can be further enhanced with fixed switching frequency operation. Simulated results confirm the feasibility of the proposal demonstrating that the performance of the system is improved with source and load currents showing a significant reduction in the harmonic distortion produced by the filter resonance.