Linear-transformation-based analysis and design of state consensus for multi-agent systems with state observers

The paper investigates the analysis and design problem of state consensus via dynamic output feedback for linear Multi-Agent Systems (MASs) under a time-invariant directed communication topology. First, a general consensus protocol with observers is adopted using the estimated state of the agent itself and the relative estimated states between neighboring agents. Then a state-linear-transformation is proposed to transform the state consensus problem into a partial stability problem. Based on the partial stability theory, a necessary and sufficient criterion for state consensus is deduced, and an explicit expression of the state consensus function is given. From the criterion, a procedure to design gain matrices in the consensus protocol is presented by applying the homotopy method to solve the involved Bilinear Matrix Inequality (BMI). Finally, a numerical example is given to illustrate the effectiveness of theoretical results.