In a proportional task allocation problem, it is desired for robotic agents to have equal duty to capability ratios. Here, this problem is addressed as a combination of deployment and consensus problems. Tasks occur in a convex region and each task is assigned to its nearest agent. Agents are deployed on this area in order to reach consensus over the value of their duty to capability ratio. A distributed, asynchronous, and scalable algorithm is presented for solving this problem in continuous time domain.

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SUMMARYThis paper addresses exponential stability of linear networked control systems. More specifically, the paper considers a continuous‐time linear plant in feedback with a linear sampled‐data controller with an unknown time varying sampling rate, the possibility of data packet dropout, and an uncertain time varying delay. The main contribution of this paper is the derivation of new sufficient stability conditions for linear networked control systems taking into account all of these factors. The stability conditions are based on a modified Lyapunov–Krasovskii functional. The stability results are also applied to the case where limited information on the delay bounds is available. The case of linear sampled‐data systems is studied as a corollary of the networked control case. Furthermore, the paper also formulates the problem of finding a lower bound on the maximum network‐induced delay that preserves exponential stability as a convex optimization program in terms of linear matrix inequalities. This problem can be solved efficiently from both practical and theoretical points of view. Finally, as a comparison, we show that the stability conditions proposed in this paper compare favorably with the ones available in the open literature for different benchmark problems. Copyright © 2012 John Wiley & Sons, Ltd.

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