Guaranteed cost synchronization for second-order discrete-time multi-node networks with switching transmission topologies and cost limitations

Abstract

The guaranteed cost synchronization control for discrete-time second-order leader-following multi-node networks with varying transmission topologies and cost limitations is investigated. First, the control law and its cost function are proposed to balance the tradeoff between the synchronization regulation and the control cost. Then, we derive the sufficient conditions without cost limitations to achieve guaranteed cost synchronization with varying transmission topologies, where the dimensions of matrix variables do not rely on the number of nodes. In addition, we calculate an upper bound on the cost consumption index, which is a function of the initial conditions. Moreover, guaranteed cost synchronization criteria are formulated for control with cost limitations, which are involved by establishing the relation between the cost limitation and the upper bound on the cost consumption index. Numerical simulation experiments were conducted to validate the theoretical results.