Observers form an integral part of output feedback control of linear and nonlinear systems. This dissertation investigates the use of observers in multi-agent systems to reduce information exchange and increase the convergence rate. Multi-agent systems have been immensely popular since the last two decades due to their broad applicability in practical problems, some of them being distributed sensor networks, formation control, and cooperative robotics. The controller for each agent is distributed in nature, which means that it only depends on the local information available to it. The distributed approach has several advantages such as less computational effort, reliability, etc., compared to the centralized one where there is a central agent that does all the computations and then makes the decision.The convergence rate of consensus algorithms is an important performance measure. We show that by using observers, we can increase the convergence rate of the consensus algorithm. The observer is used for estimating the missing links at each agent. We also study the effect of increasing network size on the consensus algorithm. For networks without a leader, the rate of convergence of the consensus protocol becomes slow for certain classes of graphs, while for networks with a single leader, the convergence rate becomes slow for undirected graphs. We design scalable consensus algorithms for first-order linear agents and second-order nonlinear heterogeneous agents where the convergence rate remains almost invariant of the network size.We consider the case of reduced information exchange in a network of nonlinear heterogeneous agents having the same relative degree r. We use observers along with feedback control to compensate for the heterogeneity at each agent. Finally, motivated by the practical application of multi-agent systems to power systems frequency synchronization, we fuse dynamic consensus algorithms with observers to achieve practical frequency synchronization under time-varying power-demand. We show that the frequency synchronization error can be made arbitrarily small by tuning controller and observer parameters.
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