Observer-based consensus of second-order multi-agent systems without velocity measurements

This paper investigates the consensus of second-order multi-agent systems without measuring the velocity states of the agents, where each agent can be either a double integrator or a harmonic oscillator. By utilizing the position information of the agents, a distributed observer-based protocol is proposed to solve the second-order consensus problem of multi-agent systems with or without time delay. The observer-based consensus problem is converted to the stability analysis for a set of second-order quasi-polynomials through coordinate transform and system decomposition. Then, some necessary and sufficient conditions are derived for reaching second-order consensus in multi-agent systems with or without time delay, respectively, and it is shown that the consensus can be achieved if and only if the communication delay is less than a critical value. Simulation examples are given to verify the theoretical analysis.