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Research Papers

# Leader-Following Consensus Control of General Linear Multi-Agent Systems With Diverse Time-Varying Input Delays

[+] Author and Article Information
Chengzhi Yuan

Mem. ASME
Department of Mechanical, Industrial
and Systems Engineering,
University of Rhode Island,
Kingston, RI 02881
e-mail: cyuan@uri.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 20, 2017; final manuscript received November 15, 2017; published online December 22, 2017. Assoc. Editor: Yunjun Xu.

J. Dyn. Sys., Meas., Control 140(6), 061010 (Dec 22, 2017) (8 pages) Paper No: DS-17-1210; doi: 10.1115/1.4038649 History: Received April 20, 2017; Revised November 15, 2017

## Abstract

This paper addresses the problem of leader-following consensus control of general linear multi-agent systems (MASs) with diverse time-varying input delays under the integral quadratic constraint (IQC) framework. A novel exact-memory distributed output-feedback delay controller structure is proposed, which utilizes not only relative estimation state information from neighboring agents but also local real-time information of time delays and the associated dynamic IQC-induced states from the agent itself for feedback control. As a result, the distributed consensus problem can be decomposed into $H∞$ stabilization subproblems for a set of independent linear fractional transformation (LFT) systems, whose dimensions are equal to that of a single agent plant plus the associated local IQC dynamics. New delay control synthesis conditions for each subproblem are fully characterized as linear matrix inequalities (LMIs). A numerical example is used to demonstrate the proposed approach.

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## References

Ren, W. , and Beard, R. W. , 2008, Distributed Consensus in Multi-Vehicle Cooperative Control, Springer-Verlag, London.
Cao, Y. , Yu, W. , Ren, W. , and Chen, G. , 2013, “An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination,” IEEE Trans. Ind. Inf., 9(1), pp. 427–438.
Ren, W. , 2008, “On Consensus Algorithms for Double-Integrator Dynamics,” IEEE Trans. Autom. Control, 53(6), pp. 1503–1509.
Liu, X. , Lu, W. , and Chen, T. , 2010, “Consensus of Multi-Agent Systems With Unbounded Time-Varying Delays,” IEEE Trans. Autom. Control, 55(10), pp. 2396–2401.
Su, Y. , and Huang, J. , 2012, “Cooperative Output Regulation of Linear Multi-Agent Systems,” IEEE Trans. Autom. Control, 57(4), pp. 1062–1066.
Khong, S. Z. , Lovisari, E. , and Rantzer, A. , 2016, “A Unifying Framework for Robust Synchronization of Heterogeneous Networks Via Integral Quadratic Constraints,” IEEE Trans. Autom. Control, 61(5), pp. 1297–1309.
Xiao, F. , and Wang, L. , 2008, “Consensus Protocols for Discrete-Time Multi-Agent Systems With Time-Varying Delays,” Automatica, 44(10), pp. 2577–2582.
Tian, Y. , and Liu, C. , 2008, “Consensus of Multi-Agent Systems With Diverse Input and Communication Delays,” IEEE Trans. Autom. Control, 53(9), pp. 2122–2128.
Sun, Y. G. , and Wang, L. , 2009, “Consensus of Multi-Agent Systems in Directed Networks With Nonuniform Time-Varying Delays,” IEEE Trans. Autom. Control, 54(7), pp. 1606–1613.
Lin, P. , and Jia, Y. , 2009, “Consensus of Second-Order Discrete-Time Multi-Agent Systems With Nonuniform Time-Delays and Dynamically Changing Topologies,” Automatica, 45(9), pp. 2154–2158.
Nuño, E. , Ortega, R. , Basañez, L. , and Hill, D. J. , 2011, “Synchronization of Networks of Nonidentical Euler-Lagrange Systems With Uncertain Parameters and Communication Delays,” IEEE Trans. Autom. Control, 56(4), pp. 935–941.
You, X. , Hua, C. , Peng, D. , and Guan, X. , 2015, “Leader-Following Consensus for Multi-Agent Systems Subject to Actuator Saturation With Switching Topologies and Time-Varying Delays,” IET Control Theory Appl., 10(2), pp. 144–150.
Megretski, A. , and Rantzer, A. , 1997, “System Analysis Via Integral Quadratic Constraints,” IEEE Trans. Autom. Control, 42(6), pp. 819–830.
Seiler, P. , 2015, “Stability Analysis With Dissipation Inequalities and Integral Quadratic Constraints,” IEEE Trans. Autom. Control, 60(6), pp. 1704–1709.
Kao, C. , and Rantzer, A. , 2007, “Stability Analysis of Systems With Uncertain Time-Varying Delays,” Automatica, 43(6), pp. 959–970.
Kao, C. , 2012, “On Stability of Discrete-Time LTI Systems With Varying Time Delays,” IEEE Trans. Autom. Control, 57(5), pp. 1243–1248.
Yuan, C. , and Wu, F. , 2017, “Exact-Memory and Memoryless Control of Linear Systems With Time-Varying Input Delay Using Dynamic IQCs,” Automatica, 77, pp. 246–253.
Eichler, A. , and Werner, H. , 2015, “Improved IQC Description to Analyze Interconnected Systems With Time-Varying Time-Delays,” American Control Conference (ACC), Chicago, IL, July 1–3, pp. 5402–5407.
Boyd, S. , Ghaoui, L. E. , Feron, E. , and Balakrishnan, V. , 2004, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.
Zhou, K. , Doyle, J. C. , and Glover, K. , 1996, Robust and Optimal Control, Prentice Hall, Englewood Cliffs, NJ.

## Figures

Fig. 1

Network graph (node 0 is the leader)

Fig. 2

Simulation results: (a) first state xi,1(t), (b) second state xi,2(t), (c) third state xi,3(t), and (d) fourth state xi,4(t)

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