Abstract
This paper investigates the leaderless <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem of multi-agent systems with higher-order Lipschitz dynamics and external disturbance. The topology is assumed to be directed. Distributed controllers using only relative outputs information of the adjacent agents are constructed. In order to deal with the non-symmetric property of the associated Laplacian matrix of directed topology, some properties of Laplacian matrix are introduced. By introducing an appropriate state transformation, the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem is converted to a low-dimensional system stability problem which is solved using Lyapunov stability analysis method. The effectiveness of the proposed control design is demonstrated through simulation examples.
Highlights
The consensus of multi-agent systems have received compelling attention due to its wide-spread applications in satellites formation [1], unmanned systems [2], and distributed reconfigurable sensor networks [3, 4]
Considering the fact that some system are usually described with nonlinear dynamics, researchers have studied the consensus problem of higher-order nonlinear multi-agent systems
It can be observed that, as for directed topology, the most of the existing conclusions of output based consensus controller for Lipschitz nonlinear multi-agent systems focus on the leader-following consensus problem [22, 23, 25]
Summary
The consensus of multi-agent systems have received compelling attention due to its wide-spread applications in satellites formation [1], unmanned systems [2], and distributed reconfigurable sensor networks [3, 4]. When the union graph having a directed spanning tree rooted at the leader, [20] considered the performance consensus tracking problem of singular Lipschitz multi-agent systems Both the leaderless and leader-following guaranteed-performance consensus problems were investigated in [21] with strongly connected and balanced topologies. It can be observed that, as for directed topology, the most of the existing conclusions of output based consensus controller for Lipschitz nonlinear multi-agent systems focus on the leader-following consensus problem [22, 23, 25]. Motivated by the above discussion, this paper aims to solve the leaderless H∞ consensus problem of Lipschitz multi-agent systems with external disturbance using output feedback under quite general communication topology conditions. To the best of our knowledge, dynamic leaderless consensus protocols using output feedback are proposed for the first time for higher-order Lipschitz nonlinear systems both with general directed topology and external disturbance.
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