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Applications of convex analysis to consensus algorithms, pointwise asymptotic stability, and its robustness


Convex analysis and the theory of differential inclusions with maximal monotone right-hand sides suggests casting consensus algorithms as systems involving switching between such differential inclusions. Convergence of solutions to such switching systems is shown and applications to consensus are presented. Robustness of pointwise asymptotic stability for a single differential inclusion which has some monotonicity-related properties, but needs not be monotone, is shown.

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