Memristor device represents one of the most relevant technologies to deal with CMOS technological issues. In the scientific literature, a relevant amount of works have discussed the memristor device, with a particular emphasis on memristor-based crossbar architectures. However, while the synthesis of combinational logic circuits is widely discussed, the same cannot be said for sequential logic circuits. In this work, we propose a new approach for synthesizing sequential circuits based on memristor crossbar, by enhancing an existing architecture. This approach only exploits memristors within the crossbar for implementing the state feedback mechanism, with the aim of advancing the integration process of memristor-based circuits. Moreover, to provide an automated synthesis process of memristor-based sequential circuits, we extend a pre-existing automated synthesis framework so it can be integrated with widely used tools and formats as register-transfer level (RTL) or Berkeley Logic Interchange Format (BLIF) files. We performed several experiments on publicly available benchmarks in order to compare the proposed architecture against its predecessor in terms of circuit integration and efficiency. Obtained results highlight acceptable overheads (up to a maximum of 24%) compared with the opportunity of integration offered by the proposed architecture.