In this study, a resilient distributed control algorithm is proposed for the secondary voltage and frequency restoration of an autonomous inverter-based microgrid considering simultaneous relative state-dependent noises and communication time-delays (CTDs). The proposed algorithm is robust against potential time-varying stochastic noises and CTDs, which corrupt the data exchanges in the secondary control layer. Additionally, this study considers the contribution of both distributed generation and distributed energy storage (DES) units in islanded AC microgrids. The presence of DES creates the need for an extra control algorithm to provide state-of-charge (SoC) balancing for these units and having precise active power-sharing. The theoretical concepts of the proposed control algorithm, including the mathematical modelling of microgrid, basic lemma, and controller design procedure, are outlined. The performance assessment of the presented control algorithm is evaluated through simulations on a test microgrid in MATLAB/Simulink software. Then, some previously-reported algorithms are selected to compare the proposed control algorithm with them. The obtained results show the effectiveness and robustness of the presented algorithm in regulating the voltage and frequency, matching SoCs, and as a result, having precise active power-sharing.