Guaranteed cost positive consensus for multi-agent systems with multiple time-varying delays and MDADT switching

This paper investigates the guaranteed cost positive consensus for linear multi-agent systems (MASs) with multiple time-varying delays and switching topologies. First, necessary and sufficient conditions for the positivity of the focused system are given. The positive consensus criterion and switching signals are derived by combining multiple Lyapunov–Krasovskii functionals with mode-dependent average dwell time approaches. Then, the guaranteed cost positive consensus is studied via the state errors among neighbouring agents and control inputs. It realizes a trade-off between the consensus regulation performance and the control energy consumption of MASs. Particularly, the determined upper bound of the cost function depends merely on the initial conditions of the agents and is independent of the switching movements. Finally, simulation results are given to validate the proposed control scheme.