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This paper proposes an approach for the solvability of multi-agent systems with Markov jumps subject to time-varying delay and uncertainties. The primary concern of this paper is to construct a state feedback control design with a guaranteed cost function which not only ensures consensus but also assures certain amount of energy consumption. This cost function is designed with the aid of control inputs of all agents and state error among neighbouring agents. A new set of sufficient conditions for the guaranteed cost consensus of the considered Markov jumping multi-agent system (MAS) is derived in terms of linear matrix inequalities (LMIs) by constructing suitable Lyapunov-Krasovskii functional (LKF) and with the aid of Kronecker product properties. Finally, a numerical example is given to illustrate the effectiveness of the developed theoretical results.

Guaranteed cost leaderless consensus for uncertain Markov jumping multi-agent systems