H∞ containment control of multi‐agent systems with mixed time‐varying delays and exogenous disturbances via observer‐based output feedback

This paper discusses the distributed containment control of Lipschitz nonlinear multi‐agent systems subject to mixed delays and exogenous disturbances, expressed by a directed topology. The existing works usually restrict the delays to constant and/or time‐varying types with uniform structures. To counter the transmission time‐varying delay in the nonlinear dynamics and memory time‐varying delay in the control input, and thus, a dynamic output feedback containment control law is proposed where the containment and observer errors eventually converge to zero. By constructing the Lyapunov–Krasovskii functionals and adopting Young's inequalities technique, the consensus conditions and gain matrices are derived. Moreover, the control law guarantees a performance index in terms of the bounded exogenous disturbances. This further motivates us to investigate the containment problems with mixed delays even if the disturbances are unbounded. Numerical simulation is performed to illustrate the proposed results.