The consensus problem of the two-layer multi-agent systems subjected to cyber-attacks was studied. Aiming at the two-layer multi-agent systems composed of the leaders' layer and the followers' layer, the situation as the following was given:the neighboring agents in the leaders' layer were cooperative, the adjacent agents in the followers' layer were cooperative or competitive, and there was a restraining relationship between some corresponding agents in the leaders' layer and the followers' layer. The consensus problem among the nodes of leaders' layer, followers' layer and two-layer multi-agent systems subjected to cyber-attack was discussed. Based on the related knowledge such as Linear Matrix Inequality (LMI), Lyapunov stability theory and graph theory, the sufficient criteria for consensus between the nodes in the leaders' layer multi-agent system, bipartite consensus between the nodes in the followers' layer multi-agent system and node-to-node bipartite consensus between the nodes in the two-layer multi-agent systems were given. Finally, the numerical simulation examples were given, and the consensus of the two-layer multi-agent systems subjected to cyber-attack was realized, which verified the validity of the proposed criteria.

Low Density Parity Check Code (LDPC) is a kind of (n, k) linear block codes. The conventional encoding method can complete the encoding work when the length of the codes is short, but as the codes become longer, the memory of computer is hard to bear when still using the common encoding methods. To solve this problem, two kinds of effective encoding and decoding schemes were proposed. Firstly, different from the traditional data parity bit decoding, the proposed data reconciliation scheme used side information and syndrome produced by the initial data to employ joint decoding. Secondly, the parity matrix was stored in a way that only the positions of 1 in the form of the cross circular list were recorded, which could greatly save memory space. At last, C implementation could improve effectiveness of the codes. Length of a block of codes in this experiment was 105. The Bit Error Ratio (BER) of codes was converged above 1.0dB, only in need of 4 seconds to decode one block, the code rate could reach 24.85kb/s when the decoder was converged. The results show that the proposed schemes have strong timeliness.