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Guaranteed-cost synchronization problems for the second-order Lipschitz nonlinear wireless sensor network with switching topologies and the given cost budget are investigated. The existing sufficient conditions for the network synchronization are usually proposed on the basis of linear matrix inequality (LMI) tools without taking given cost budgets into account. First, this paper designs a network synchronization protocol with a guaranteed-cost constraint, where the tradeoff between the battery power consumption and the network synchronization performance is established. Second, by the structure characteristic of a piecewise continuous matrix and the Lipschitz condition, the nonlinear term of the dynamics is linearized. Then, sufficient conditions are developed to make the Lipschitz nonlinear network reach guaranteed-cost synchronization, and an upper bound of the cost function is derived for the case not considering the given cost budgets. Third, for the case where the whole energy supply is limited, the relationship between the practical energy consumption and the given limited cost budget is drawn to the criterion as a cost constraint, which can make the nonlinear network reach guaranteed-cost synchronization. In particular, the explicit expressions of control gains in these criteria are derived, which indicates that the existence of control gains in network synchronization criteria can be ensured and most existing references cannot deal with the analytic solutions of control gains. In addition, the proposed criteria depend upon the minimum nonzero and maximum eigenvalues, which means that the scalability of the wireless sensor network can be ensured. Finally, the theoretical results are illustrated by numerical simulations.

Guaranteed-Cost Synchronization for Second- Order Wireless Sensor Networks With Nonlinear Dynamics and Given Cost Budgets