In islanded microgrids, voltage source inverters working in parallel are expected to provide regulation of the local frequency while granting active power sharing. This paper presents a local control approach at each inverter based on an event-driven operation of a parameter-varying filter. It ensures perfect active power sharing and controllable accuracy for frequency restoration without requiring the exchange of control data between inverters over the communication network. This paper includes stability analysis and design guidelines for the control parameters using a modeling approach that considers the interaction between inverters. Selected experimental results on a three-inverter laboratory microgrid corroborate the effectiveness of the proposed control scheme, and outlines its advantages with respect to previous similar schemes and the performance cost that implies not using communications.