Abstract
Consensus of first-order and second-order multiagent systems has been wildly studied. However, the convergence of high-order (especially the third-order to the sixth-order) state variables is also ubiquitous in various fields. The paper handles consensus problems of high-order multiagent systems in the presence of multiple time delays. Obtained by a novel frequency domain approach which properly resolves the challenges associated with nonuniform time delays, the consensus conditions for the first-order and second-order systems are proven to be nonconservative, and those for the third-order to the sixth-order systems are provided in the form of simple inequalities. The method revealed in this article is applicable to arbitrary-order systems, and the results are less conservative than those based on Lyapunov approaches, because it roots in sufficient and necessary criteria of stabilities. Simulations are carried out to validate the theoretical results.
Highlights
Consensus problems of multiagent systems have found many applications in the fields that hold great promise, including biosciences, robotics, and computer sciences
Obtained by a novel frequency domain approach which properly resolves the challenges associated with nonuniform time delays, the consensus conditions for the first-order and second-order systems are proven to be nonconservative, and those for the third-order to the sixth-order systems are provided in the form of simple inequalities
The present work first brings out sufficient consensus conditions for the first-order to sixth-order nonuniformly delayed systems which are most likely to apply to practical engineering applications [28]: if all the delays are bounded by a given value and all the parameters agree to corresponding inequalities, the systems can achieve consensus and in addition, for the sake of nonconservativeness, the paper provides stronger conditions for the first-order and second-order systems by thorough derivation: the states converge when all the delays are bounded by a given value but diverge when all the delays exceed that value
Summary
Consensus problems of multiagent systems have found many applications in the fields that hold great promise, including (but not limited to) biosciences, robotics, and computer sciences. The present work first brings out sufficient consensus conditions for the first-order to sixth-order nonuniformly delayed systems which are most likely to apply to practical engineering applications [28]: if all the delays are bounded by a given value and all the parameters agree to corresponding inequalities, the systems can achieve consensus and in addition, for the sake of nonconservativeness, the paper provides stronger conditions for the first-order and second-order systems by thorough derivation: the states converge when all the delays are bounded by a given value but diverge when all the delays exceed that value. Literature [29] has proposed a high-order nonlinear consensus tracking algorithm with unmeasurable system states which applies to wide-range multiagent systems and proven the achievement of consensus by constructing Lyapunov functions, while time delays are not considered. In [9], Zhang et al have solved average consensus problem of high-order multiagent system with time-varying delays and provided stability conditions in the form of LMIs via a LyapunovKrasovskii approach. The remainder of this note is organized as follows: Section 2 states the consensus problem with the help of graph theory; Section 3 presents the main results by demonstrating the stability analysis; Section 4 depicts the selected simulation experiments; Section 5 draws conclusions with future research directions
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