On the consensus tracking investigation for multi-agent systems on time scale via matrix-valued Lyapunov functions

Self Cite

The problem of distributed leader-follower consensus for second-order linear multiagent systems with unknown nonlinear inherent dynamics is investigated in this paper. It is assumed that the dynamic of each agent is described by a semilinear second-order dynamic equation on an arbitrary time scale. Using calculus on time scales and direct Lyapunov's method, some sufficient conditions are derived to ensure that the tracking errors exponentially converge to zero. Some numerical results show the effectiveness of the proposed scheme.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed leader‐follower consensus for a class of semilinear second‐order multiagent systems using time scale theory

Babenko

Defoort

Djemaï

et al. 2018

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“…Moreover, the time‐scale theory shows its advantage in analyzing the Zeno solutions of hybrid systems, which was relatively difficult in the traditional two‐dimensional hybrid domain 28 . Recently, considerable results about systems on time scales have been presented in the literatures, 29‐37 etc. However, little attention has been paid to stability problem of positive systems on time scales.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of positive switched impulsive systems with delay on time scales

Lü

Wang

et al. 2020

In this paper, stability analysis of positive switched impulsive systems with delay on time scales is investigated. Firstly, a necessary and sufficient condition is provided for positivity of the considered systems. Secondly, by respectively considering the situations that the switching behavior and the impulsive phenomenon happen simultaneously and asynchronously, the uniformly asymptotical stability problems are addressed. Then, based on the linear copositive Lyapunov-Krasovskii functional technique, two less conservative stability criteria are proposed. It are shown that these two criteria allow the timescale derivative of related Lyapunov functionals to be non-negative at some intervals. Moreover, these two criteria are effective for not only continuous cases and discrete cases, but also some other positive switched impulsive systems on general uniform or hybrid time domains. Finally, a non-continuous and non-discrete example is given to illustrate the effectiveness of the theoretic results. K E Y W O R D S positive switched impulsive systems, stability, time scale 1 INTRODUCTION Positive systems play an important role in many practical areas, such as economics, populations dynamics, ecology and Boolean network, etc. 1-7 The distinctive characteristics of this kind of systems are that their state variables, inputs and outputs take only nonnegative values. The common approaches for stability analysis of linear time-invariant positive systems are the Hurwitz criterion, the Routh criterion, and the Lyapunov technique (including the linear copositive Lyapunov function theorem and the diagonal quadratic Lyapunov function method). 2 And the Lyapunov function approach has been successfully introduced to stability analysis of nonlinear or delayed positive systems. 8,9 Recently, several other kinds of positive systems have also received continued attention, such as switched positive systems, 10-14 impulsive positive systems, 15-19 and switched impulsive positive systems, 20-23 etc. When studying switched impulsive positive systems, a natural question is that do the switching behavior and the impulsive phenomenon happen simultaneously or asynchronously? Unfortunately, the literatures 21-23 only consider the former. Actually, from the viewpoint of reality, it is more reasonable to consider the latter. Moreover, in, 21-23 the necessary conditions for analyzing stability of switched impulsive positive systems are to construct Lyapunov functionals with time-derivative or time-shift being strictly negative. However, this requirement can be surely weakened by the ideas in. 24,25 Generally speaking, continuous positive systems and discrete positive systems are always investigated separately. As far back as 1937, the work 26 stated that a major task of mathematics was to harmonize the continuous and the discrete, to

“…The consensus of multiagent systems (MASs) widely appears in a variety of scenarios, to mention a few, flocking, containment, tracking, formation, etc. Generally, the objective of consensus is to find a control protocol that enables all of the agents to reach an agreement on certain interest by local information exchange among agents …”

Section: Introductionmentioning

confidence: 99%

Bounded consensus for multiagent systems by event‐triggered data transmission, time delay, and predictor‐based control

Cui

2019

Summary This paper investigates the consensus issue of multiagent systems with data transmission time delay. The state measurement of each local agent is directly sent to a private event‐trigger and further authorized to be broadcasted to its neighbors via communication network only when the threshold of the event‐trigger is violated. Since the controller always receives discrete‐time neighbor information with data transmission time delay, a predictor is employed to estimate the continuous‐time neighbor state. Based on the estimated state, a novel consensus protocol is mainly proposed for achieving the bounded consensus of the multiagent systems. By the proposed method, the asynchronous neighbor information is allowed and the margin of data transmission time delay is also given. Furthermore, it has been proved that the unwanted Zeno phenomena can be naturally excluded. Numerical example is provided to demonstrate the effectiveness of the proposed method.