Abstract
This paper studies consensus and \(H_\infty\) consensus problems for heterogeneous multi-agent systems composed of first-order and second-order integrator agents. We first rewrite the multi-agent systems into the corresponding reduced-order systems based on the graph theory and the reduced-order transformation. Then, the linear matrix inequality approach is used to consider the consensus of heterogeneous multi-agent systems with time-varying delays in directed networks. As a result, sufficient conditions for consensus and \(H_\infty\) consensus of heterogeneous multi-agent systems in terms of linear matrix inequalities are established in the cases of fixed and switching topologies. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.
Highlights
In recent years, the consensus control of multi-agent systems has attracted much attention, due to its broad applications in communication, system control theory, applied mathematics, design of sensor networks, computer science, and so on
Most multi-agent systems considered in the literature are homogeneous, that is all of the agents have the same dynamics behavior
There are very few results on the consensus of heterogeneous multi-agent systems, except Zheng and Wang [15,16,17], where consensus problems of a heterogeneous multi-agent system were studied by applying the graph theory and the Lyapunov direct method
Summary
The consensus control of multi-agent systems has attracted much attention, due to its broad applications in communication, system control theory, applied mathematics, design of sensor networks, computer science, and so on. In many practical applications involving multi-agent systems, the communication delay [18,19,20,21,22,23], leader-following networks [24,25,26], discrete-time [27,28,29], as well as H∞ consensus problems [30,31,32] should be considered in the consensus of multi-agent systems. In this work, we investigate the consensus and H∞ consensus problems for heterogeneous multi-agent systems in fixed and switching topologies with a time delay. Because of the complexity of the heterogeneous multi-agent system with time-delays, many existing methods for the consensus of the first-order and the second-order multi-agent systems become invalid. The purpose of this paper is to establish consensus and H∞ consensus criteria for heterogeneous multi-agent systems by applying the linear matrix inequality technique. L2 [0, ∞) denotes the space of square-integrable vector functions over [0, ∞)
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