Formation Problem of Multi-Agent Systems with Switching Topologies and Time Delays in Flocking

Formation in flocking is universal. In this paper, we discuss formation in flocking without leaders. Both constant time delays and variable time delays are considered. Switching topologies are considered for multi-agent system. Our aim in the paper is to solve formation under time delays in inputs and agents in the double integrators. First, Liapunov-Razumikhin theorem is applied in formation when inputs are affected by constant time delay. Second, Linear Matrix inequality method is used to formation when inputs are affected by variable time-delay.