Sampled‐data consensus of multiagent systems with switching jointly connected topologies via time‐varying Lyapunov function approach

Abstract

SummaryConsensus problem of multiagent systems with switching jointly connected topologies under sampled‐data control is studied in this article. The main contribution is that the consensus problem for such system is solved without the assumption that the system matrices are stable or critically stable. For this purpose, a time‐varying Lyapunov function method is utilized to describe the state characteristics with switching jointly connected topologies. Based on the time‐varying matrix of Lyapunov function, the “decline” characteristics at the switching instants is derived to compensate the divergence among the agents with disconnected topologies. Utilizing the “decline” characteristics, the overall consensus of such system can be guaranteed in the framework of dwell time. Finally, the effectiveness of the proposed result is illustrated by two numerical examples.

Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

“…It has overcome the traditional 'jump' phenomenon at switching instants for multiple Lyapunov functions [19,29]. But in this study, it is difficult to derive condition (12) at all the switching instants T r since there exist discrete signals generated by event-triggered control and such discrete signals are not measurable with time. To overcome this difficulty, we propose the periodic-sampling time unit (PSTU) approach to study this case.…”

“…Assuming ϵ q (t) = 1 and ϵ k (t) = 0 when t ∈ [T r , T r + 1 ), then we can (11). Then supposing that the functions switch from mode q to mode k at instant T r + 1 , we have V(T r + 1 + ) ≤ μV(T r + 1 − ) from (12). It also implies V(T r + 1 ) ≤ μe −α(T r + 1 − T r ) V(T r ).…”

“…, where k ≠ r, ∀k, r ∈ P, which can satisfy condition (12) in Lemma 1. In this way, through choosing appropriate piecewise Lyapunov matrices, the jump phenomenon at the switching instants in the existing results can be eliminated and the decrease characteristics at each switching instant can be derived.…”

“…This is one of the main contributions in this paper. In fact, many conditions can satisfy condition (12) in Lemma 1. In the process of proving Theorem 1, condition (26) is given to satisfy condition (12).…”

“…Consensus is an important behaviour in multi-agent systems, where the agents depend on the relative positions of its neighbours and reach an agreement on a common value [7]. Recent years, oceans of papers and applications have witnessed the flourishing evolution of consensus for multi-agent systems [8][9][10][11][12][13]. In the early work, contributions of the consensus for multi-agent systems were focused on the fixed communication topology [14][15][16].…”