Abstract
This paper is concerned with the optimal consensus problem of multi-agent systems (MASs) with general unstable linear dynamics. The main tool for the design and analysis is the inverse optimality and set stability theory. Firstly, the optimal conditions for ensuring set stability are developed for discrete-time linear systems in terms of the inverse optimality principle. Then for the MASs with unstable dynamics, the approach to designing the optimal consensus protocol is proposed, and the detailed design conditions are developed. Based on the set stability theory, the consensus properties are proved. Finally, a simulation study is provided to verify the effectiveness of the proposed method.
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