Extended consensus algorithm for multi-agent systems

The authors study an extended consensus problem for multi-agent systems, where the entire system is decentralised in the sense that each agent can only obtain information (states) from its neighbour agents. The concept'extended consensus'means that a combination of each agent's state elements is required to converge to the same vector. For this extended consensus problem, they propose to reduce the problem to a stabilisation problem with an appropriate transformation, and obtain a strict matrix inequality with respect to a Lyapunov matrix and a structured controller gain matrix. The authors then utilise a homotopy-based method for solving the matrix inequality effectively, and show the validity of the result by an example. The feature of the present algorithm is that it can deal with various additional control requirements such as convergence rate specification and actuator limitations.