Leader-following consensus of second-order multi-agent systems with time-varying delays and arbitrary weights

Abstract

Using Lyapunov first method instead of traditional Lyapunov second method, this paper focuses on studying the consensus tracking control problem of multi-agent systems (MASs) with time-varying delays and arbitrary adjacent weights under fixed topology and switching topology, respectively. We first give four equivalent criteria for MASs with fixed communication topology, where the positive stability of matrix [Formula: see text] ( L is the Laplacian matrix of [Formula: see text], B is the leader’s adjacency matrix) not only plays a key role as usual but also becomes an urgent and more complicated problem due to the introduction of negative weights in MASs. Second, for MASs with switching communication topology if the average dwell time of switching topology, the total activation time of stable subsystems and the upper bound of time delay satisfy some conditions, then MASs with all stable subsystems (partially stable subsystems) can achieve consensus tracking. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.

A Consensus Control for a Multi-Agent System With Unknown Time-Varying Communication Delays

“…The corresponding delays change periodically from 0.1 to 0.6. The figure-2 shows the state trajectories resulting from (20) and (26). It shows that both consensus protocols achieve asymptotic bounded consensus.…”

“…The proposed consensus control was compared with the existing state of art method [26] in figure -7. Due to the limited applicability of the control in [26] which was developed for a MAS with a time-varying state delay, every communication delay on the link in the figure-1 was set as 0.5 cos(t) + 0.5.…”

“…The proposed consensus control was compared with the existing state of art method [26] in figure -7. Due to the limited applicability of the control in [26] which was developed for a MAS with a time-varying state delay, every communication delay on the link in the figure-1 was set as 0.5 cos(t) + 0.5. The velocity of the leader agent was set as the constant velocity of 20m/s, since the consensus control in [26] was developed with the assumption that the leader moves at a constant velocity.…”

“…Proof: The consensus control given in (26) results in the same dynamics in the sliding surface as with known delay. Thus, q x is upper bounded by a finite value, which proves the proposition.…”

“…A leader-follower consensus protocol for a MAS with partial mixed impulses and unknown same time-varying state delay was proven to achieve exponential consensus under a specific condition [25]. A simple consensus protocol for a second-order leaderfollower MAS with unknown same time-varying input delay was shown to achieve consensus as long as the maximum delay is less than a threshold determined by a consensus condition [26]. A delay partitioning method and Wirtingerbased inequality were exploited to derive a second order consensus control for a MAS with unknown time varying input delay, of which sufficient condition for an asymptotic consensus was less conservative [27].…”