Abstract
The average consensus in undirected networks of multi-agent with both fixed and switching topology coupling multiple time-varying delays is studied. By using orthogonal transformation techniques, the original system can be turned into a reduced dimensional system and then LMI-based method can be applied conveniently. Convergence analysis is conducted by constructing Lyapunov-Krasovskii function. Sufficient conditions on average consensus problem with multiple time-varying delays in undirected networks are obtained via linear matrix inequality (LMI) techniques. In particular, the maximal admissible upper bound of time-varying delays can be easily obtained by solving several simple and feasible LMIs. Finally, simulation examples are given to demonstrate the effectiveness of the theoretical results.
Highlights
More and more researchers have paid a great deal of attention on distributed coordinated control of networks of dynamic agents within the control community
Sufficient conditions on average consensus problem with multiple time-varying delays in undirected networks are obtained via linear matrix inequality (LMI) techniques
The original system is turned into a reduced dimensional system by orthogonal transformation; Secondly, via constructing a different Lyapunov-Krasovskii function, a sufficient condition expressed as LMI is proposed to guarantee all agents reach average consensus in fixed and switching network
Summary
More and more researchers have paid a great deal of attention on distributed coordinated control of networks of dynamic agents within the control community. In [8], Saber provided a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. Time-varying delay has been extensively considered for the cases of multi-agent undirected and/or direction networks with fixed and/or switching topology [17,18] and [19]. The studies on consensus problem of multi-agent networks with multiple timevarying delays are still sparse In this case, theoretical analysis is more challenging. In [20], the authors proposed a consensus protocol for multi-agent undirected network with multiple time-varying delays based on LMI method.
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