Abstract: Highlights•The concept of guaranteed cost is introduced to incorporate with event based control to further investigate the energy consumption.•A novel event based consensus approach is applied to general LTI multi-agent systems.•The controller gain matrix and the triggering parameters with guaranteed cost performance are co-designed to achieve the consensus for distributed multi-agent systems.•A BMI (bilinear matrix inequality) based approach is used to reduce the conservativeness of controller design.
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