Guaranteed cost consensus problems for general linear multi-agent systems with switching topologies are investigated, where both the jointly-connected and connected switching topologies are considered. Each interaction topology in the interaction topology set may not be connected and the union topology in each finite time interval is connected for the jointly-connected switching topology, while each interaction topology is connected for the connected switching topology. In the guaranteed cost consensus problem, a guaranteed cost function is constructed to represent the consensus regulation performance and the control energy consumption. By the state space decomposition approach and some mathematics tools, several sufficient conditions for guaranteed cost consensus with switching topologies are given and design methods for the consensus control gain matrix are presented. When all the general linear dynamic systems achieve guaranteed cost consensus, an upper bound is given for the introduced guaranteed cost function and the consensus function represented the whole motion of all dynamic systems is determined. The effectiveness of the proposed results is demonstrated by numerical simulations.
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