Consensus is a central issue in designing multi-agent systems (MASs). How to design control protocols under certain communication topologies is the key for solving consensus problems. This thesis is focusing on investigating the consensus protocols under different scenarios:​ (1) The second-order system dynamics with Markov time delays;​ (2) The Euler-Lagrange dynamics with uniform and nonuniform sampling strategies and the event-based control strategy.

Chapter 2 is focused on the consensus problem of the multi-agent systems with random delays governed by a Markov chain. For second-order dynamics under the sampled-data setting, we first 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 (LMIs), we analyze the mean square stability of the error system dynamics with fixed communication topology. 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. Finally, by applying an augmentation technique, we convert the error system dynamics to a delay-free stochastic system. A sufficient condition is established to guarantee the consensus of the networked multi-agent systems with switching topologies. Simulation studies for a fleet of unmanned vehicles verify the theoretical results.

In Chapter 3, we propose the consensus control protocols involving both position and velocity information of the MASs with the linearized Euler-Lagrange dynamics, under uniform sampling and nonuniform sampling schemes, respectively. Then we extend the results to the case of applying the centralized event-triggered strategy, and accordingly analyze the consensus property. Simulation examples and comparisons verify the effectiveness of the proposed methods.