This paper proposes a consensus algorithm for continuous-time single-integrator multi-agent systems with relative state-dependent measurement noises and time delays in directed fixed and switching topologies. Each agent's control input relies on its own information state and its neighbors' information states, which are delayed and corrupted by measurement noises whose intensities are considered a function of the agents' relative states. The time delays are considered time-varying and uniform. For directed fixed topologies, condition to ensure mean square linear -consensus (average consensus, respectively) are derived for digraphs having spanning tree (balanced digraphs having spanning tree, respectively). For directed switching topologies, conditions on both time delays and dwell time have been given to extend the mean square linear -consensus (average consensus, respectively) of fixed topologies to switching topologies. 861In references [1][2][3][4][5][6][7][8][9], the noises are considered additive noises whose intensities are constant and independent of the agents states. Recently, some research [10-12] considered a more reliable and practical model for the noises, which relies on the fact that the noises intensities are time-varying and dependent on the agents' states. [10] obtained sufficient conditions to ensure both mean square and almost sure consensus of high-dimensional first-order dynamics under relative state-depending measurement noises in undirected topologies, where the noise intensities are assumed a vector or a matrix function of agents' relative states.[11] studied the single-integrator consensus with measurement noises in directed topologies. The measurement noise intensities are considered a linear function proportional to the absolute agents' relative states. Conditions to achieve mean square convergence and strong convergence have been obtained for both fixed and time-varying topologies.[12] extended the results of [11] to the leader-following consensus in directed fixed and switching topologies and derived conditions to ensure the tracking in mean square.Motivations and contributions: The authors in [10][11][12] assumed that the information states obtained by an agent from its neighbors are undelayed. However, this statement is not practical because the communication in real physical systems is always subject to time delays caused by the limitation of the speed of acquisition and transmission [13]. Therefore, it is of great importance if one studies the problem of consensus under relative state-dependent measurement noises and time delays. To the best of our knowledge, this problem is not investigated in the literature. In fact, solving this problem is more challenging and is not trivial, because the closed-loop equation that describes the system is a stochastic delay differential equation that is difficult to analyze, because its perturbed term is also a function of the delayed relative states, and therefore, the usual techniques that are typically used with non-state depending measurement...

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