Bipartite Fault-Tolerant Consensus of Discrete-Time Singular Multi-Agent Systems: An Observer-Based Approach

This paper studies on the bipartite fault-tolerant state consensus control problem of discrete-time singular multi-agent systems via distributed observer-based approach. Under a cooperative-competition directed topological network, a more general process fault model that can describe multiple types of faults is firstly constructed. Then a new distributed simultaneous state and fault observer is designed based on the output measurement sign error between neighboring agents. Based on this observer-based approach, the bipartite fault-tolerant control protocol via output feedback is presented based upon Gerschgorin circle theorem and discrete singular algebraic Riccati equation. With the designed control coupling gain with system topological matrix, the global closed-loop error system can be included in the stable region of the unit circle and achieve stability in the discrete-time sense. Therefore, the agents of two opposite subgroups under the signed directed graph can achieve desired bipartite consensus regardless of process faults and discrete singular dynamics. Finally, a simulation example is given to verify the feasibility and effectiveness of the proposed algorithm.