In this paper, a Lyapunov function based decentralized control scheme is proposed for a single-phase parallel-connected inverters system within islanded micro-grid. With this novel method, a proper voltage regulation (e.g., amplitude and waveform quality) and excellent power and current sharing performance can be well ensured even in the presence of unknown line impedance and unbalanced LC filter parameters. In addition, high reliability and robustness can be guaranteed since no inter-communication among inverters as well as no centralized controller is demanded, which also delivers advantages of scalability and redundancy. The stability of the closed-loop system is ensured by standard Lyapunov method. The designation of the decentralized controller is simple to implement but rather effective. Detailed simulation and hardware-in-the-loop (HIL) experimental results are presented to validate the feasibility of the proposed scheme under different operating conditions.