Output Feedback Controller Design for Multi-Agent Systems with Dynamic Heterogeneity in the Presence of Parameter Uncertainty and Exogenous Disturbances

Subject Areas : Time delay systems

Badrozaman Hosseini ¹ (MSc - Senior Engineer, Nigtcdist 2, Isfahan, Iran)
Mehdi Sojoodi ² (Assistant Professor – Department of Electrical Engineering, Tarbiat Modares University)

Received: 2014-06-28 Accepted : 2014-09-15 Published : 2014-12-01

Keywords: LMI, Jenson's inequality, H∞ robust stability, dynamic output feedback, interval time varying delay,

Abstract :

This paper is concerned with network based leader following consensus for a distributed multi agent system with interval time varying delays in the presence of uncertainty and disturbances. A network based consensus control protocol under a directed graph is proposed. The nonlinear time varying coefficients derived from Jenson's integral inequality is approximated with an estimation method. Finally with convex combination, less conservative stability criteria are provided. In this method, the output feedback H∞ control is proposed to leader following consensus and robust stability of the closed loop system. In the presence of uncertainty and disturbances in the system, using H∞ control along with dynamic output feedback controller has led to better results in tracking the reference signal. This study provides H∞inf stability criteria in the forms of linear matrix inequalities (LMIs) and convex programming standard form. Numerical examples are given to show the effectiveness of the obtained theorems and results.

References:

[1] L. Ding, Q.L. Han, G. Guo, "Network-based leader-following consensus for distributed multi-agent systems", Automatica, Vol. 49, No. 7, pp. 2281-2286, July 2013.

[2] Y. Hu, P. Li, J. Lam, "Consensus of multi-agent systems: a simultaneous stabilization approach", IET Control Theory and Applications, Vol. 6, No. 11, pp. 1758-1765, 2012.

[3] A. Papachristodoulou, M.M. Peet, S.I. Niculescu, "Stability analysis of linear systems with time-varying delays: delay uncertainty and quenching", Proceeding of the IEEE/CDC, Vol. 12, pp. 2117-2122, 2007.

[4] M. Tang, Y.W. Wang, C. Wen, "Improved delay-range-dependent stability criteria for linear systems with interval time-varying delays", IET Control Theory and Applications, Vol. 6, No. 6, pp. 868-873, 2012.

[5] M.C. De Oliveira, J.C. Geromel, L. Hsu, "LMI characterization of structural and robust stability", Linear Algebra and its Applications, Vol. 296, pp. 27-38, 1999.

[6] H. Shao, "New delay-dependent stability criteria for systems with interval delay", Automatica, Vol. 45, No. 3, pp. 744-749, March 2009.

[7] P.L. Liu, "Further improvement on delay-range-dependent stability results for linear systems with interval time-varying delays", ISA Transactions, Vol. 52, No. 6, pp. 725-729, 2013.

[8] F. Souza, "Further improvement in stability criteria for linear systems with interval time-varying delay", IET Control Theory and Applications, Vol. 7, No. 3, pp. 440-446, 2013.

[9] N.T. Thanh, V.N. Phat, "H_∞ control for nonlinear systems with interval non-differentiable time-varying delay", European Journal of Control, Vol. 19, No. 3, pp. 190-198, May 2013.

[10] N.T. Thanh, V.N. Phat, "Decentralized stability for switched nonlinear large-scale systems with interval time-varying delays in interconnections", Nonlinear Analysis: Hybrid Systems, Vol. 11, pp. 22-36, 2013.

[11] V.N. Phat, Y. Khongtham, K. Ratchagit, "LMI approach to exponential stability of linear systems with interval time-varying delays", Linear Algebra and its Applications, Vol. 436, pp. 243-251, 2012.

[12] X. Zhu, Y. Wang, G. Yang, "New stability criteria for continuous-time systems with interval time-varying delay", IET Control Theory and Applications, Vol. 4, No. 6, pp. 1101-1107, 2010.

[13] L. YU, J. Wang, "Distributed robust output regulation for multi-agent systems with unknown communication delays", Proceeding of the IEEE/CCC, pp. 2838-2843, Hefei, July 2012.

[14] M.R. Davoodi, K. Khorasani, H.A.Talebi, "A novel distributed robust fault detection and isolation filter design for a network of nonhomogeneousmulti-agentsystems", Proceeding of the IEEE/CDC, pp.592-599, Maui, HI, Dec. 2012.

[15] Y. Hu, "Consensus control of multi-agent systems", University of Hong Kong, 2012.

[16] H.R. Karimi, M. Zapateiro, N. Luo, "A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations", Journal of the Franklin Institute, Vol. 347, pp.957-973, 2010.