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**1 - 3**of**3**### Characterizing Convergence Speed for Consensus Seeking over Dynamically Switching Directed Random Networks

"... Abstract — Characterizing convergence speed is one of the important research challenges in the design of distributed consensus algorithms for networked multi-agent systems. In this paper, we consider a group of agents that communicate via a dynamically switching directed random network. Each link in ..."

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Abstract — Characterizing convergence speed is one of the important research challenges in the design of distributed consensus algorithms for networked multi-agent systems. In this paper, we consider a group of agents that communicate via a dynamically switching directed random network. Each link in the network, which represents the directed information flow between any ordered pair of agents, could be subject to failure with certain probability. Hence we model the information flow using dynamic random digraphs. We characterize the convergence speed for the distributed discrete-time consensus algorithm over a variety of random networks with arbitrary weights. In particular, we propose the per-step (mean square) convergence factor as a measure of the convergence speed and derive the exact value for this factor. Numerical examples are also given to illustrate our theoretical results. I.

### An Entropy-based Metric to Quantify the Robustness of Power Grids against Cascading Failures

"... The cascading failure phenomenon in a power grid is related to both the structural as-pects (number and types of buses, density of transmission lines and interconnection of com-ponents), and the operative state (flow distribution and demand level). Existing studies most often focus on structural asp ..."

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The cascading failure phenomenon in a power grid is related to both the structural as-pects (number and types of buses, density of transmission lines and interconnection of com-ponents), and the operative state (flow distribution and demand level). Existing studies most often focus on structural aspects, and not on operative states. This paper proposes a new metric to assess power network robustness with respect to cascading failures, in particular for cascading effects due to line overloads under targeted attacks. The metric takes both the effect of structural aspects and the effect of the operative state on network robustness into ac-count, using an entropy-based approach. IEEE test systems and real world UCTE networks are used to demonstrate the applicability of this robustness metric.

### MULTI-GROUP CONSENSUS OF HETEROGENEOUS FRACTIONAL-ORDER NONLINEAR AGENTS VIA PINNING CONTROL

"... The present work concerns the multi-group consensus be-havior of directed complex networks. The network consists of a-gents with heterogeneous fractional-order non-linear dynamics. It can be divided into several groups due to their dynamics or e-quilibriums. Each group will be stabilized at an equil ..."

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The present work concerns the multi-group consensus be-havior of directed complex networks. The network consists of a-gents with heterogeneous fractional-order non-linear dynamics. It can be divided into several groups due to their dynamics or e-quilibriums. Each group will be stabilized at an equilibrium and different groups may have different steady state values. A nec-essary and sufficient condition is provided for the proposed pin-ning control law to be locally Mittag-Leffler stable. The conclu-sion turns to guarantee the exponential stable for integer-order systems. The collection of heterogeneous equilibriums is deter-mined by the geometric multiplicity of the zero eigenvalue respect to the graph Laplacian. Simulations on fractional-order chaotic systems demonstrated the conclusions.