Consensus in second-order multiple flying vehicles with random delays governed by a Markov chain

The purpose of this study is to investigate the consensus problem of multiple flying vehicles with random delays governed by a Markov chain. For second-order system dynamics under the sampled-data setting, we convert the consensus problem to the stability analysis of the equivalent error system dynamics. By designing a suitable Lyapunov function and deriving a set of linear matrix inequalities, we analyze the mean square stability of the error system dynamics. Since the transition probabilities in a Markov chain are sometimes partially unknown, we propose a method of estimating the delay for the next sampling time instant. We explicitly give a lower bound of the probability for the delay estimation which can ensure the stability of the error system dynamics. Using an augmentation technique, we convert the random time-delay discrete-time systems to delay-free stochastic systems. And then a sufficient condition is given to guarantee the consensus of the networked multi-agent system. Simulation studies for a fleet of unmanned flying vehicles verify the theoretical results.