Almost sure consensus for multi-agent systems with two level switching

In most literatures on the consensus of multi-agent systems (MASs), the agents considered are time-invariant. However in many cases, for example in airplane formation, the agents have switching dynamics and the connections between them are also changing. This is called two-level switching in this paper. We study almost sure (AS) consensus for a class of two-level switching systems. At the low level of agent dynamics, switching is deterministic and controllable. The upper level topology switching is random and follows a Markov chain. The transition probability of the Markov chain is not fixed, but varies when low level dynamics changes. For this class of MASs, a sufficient condition for AS consensus is developed in this paper.