Robust ${H_\infty}$ Guaranteed Cost Time-Varying Formation Tracking for High-Order Multiagent Systems With Time-Varying Delays

Robust <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> guaranteed cost time-varying formation tracking problems for high-order multiagent systems with external disturbances and time-varying delays are considered. It is required that the followers’ states need to track the leader’s state and to actualize the desired time-varying formation simultaneously. First, this paper devises a linear time-varying formation tracking protocol considering the effects of the delays constituted by the neighboring information. Then, an integral linear quadratic cost function constructed by the control input constraint and the formation tracking error constraint is utilized to analyze the suboptimal robust <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> guaranteed cost time-varying formation tracking performance. Third, sufficient conditions for actualizing the guaranteed cost time-varying formation tracking with <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> disturbance attenuation performance are derived, and the conditions for the feasible time-varying formation tracking are raised. To obtain the gain matrix of the protocol, only four linear matrix inequalities are required to be solved. Finally, a numerical simulation example reveals the effectiveness of the acquired results, where five agents achieve the robust <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> guaranteed cost time-varying formation tracking.