Consensus of Multi-Agent Singular Systems by Using an Algebraic Transformation

This paper delves into the consensus problem for singular multi-agent systems with a fixed communication topology whereby each agent is represented by a linear singular dynamic system. First, it is shown that singular systems can be described by standard input derivative systems. Then, due to the presence of input derivatives, an algebraic transformation is applied to eliminate the derivative inputs and to obtain an equivalent standard state space representation for multi-agent singular systems. This elimination transfers the input derivative in the output equation, which does not interfere with the consensus process. Thus, when the algebraic transformation is employed, the consensus protocol for the available network of linear dynamic agents is accommodated, which allows the agents to agree in a distributed and cooperative fashion. An example is provided to demonstrate the effectiveness of our theoretical results.