Abstract
We apply the linear matrix inequality method to consensus andH∞consensus problems of the single integrator multiagent system with heterogeneous delays in directed networks. To overcome the difficulty caused by heterogeneous time-varying delays, we rewrite the multiagent system into a partially reduced-order system and an integral system. As a result, a particular Lyapunov function is constructed to derive sufficient conditions for consensus of multiagent systems with fixed (switched) topologies. We also apply this method to theH∞consensus of multiagent systems with disturbances and heterogeneous delays. Numerical examples are given to illustrate the theoretical results.
Highlights
In recent years, decentralized coordination of multiagent systems has received many researchers’ attention in the areas of system control theory, biology, communication, applied mathematics, computer science, and so forth
To the best of our knowledge, little has been known about the H∞ consensus problem for the single integrator multiagent systems with heterogeneous time-varying delays and directed network topologies
Unlike the case of identical delays, the multiagent system with heterogeneous delays usually cannot be transformed to a reduced-order system
Summary
In recent years, decentralized coordination of multiagent systems has received many researchers’ attention in the areas of system control theory, biology, communication, applied mathematics, computer science, and so forth. To the best of our knowledge, little has been known about the H∞ consensus problem for the single integrator multiagent systems with heterogeneous time-varying delays and directed network topologies. Another purpose of this paper is to establish H∞ consensus criteria in the cases of heterogeneous delays and directed fixed topology (or switching topologies) by using the linear matrix inequality technique. These results are extended to the case of switching topologies. L2[0, ∞) denotes the space of square-integrable vector functions over [0, ∞)
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