Robust Control for Discrete-Time Sector Bounded Systems with Time-Varying Delay

Authors: Ju H. Park, S.M. Lee

Abstract:

In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.

Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075509

References:

[1] P. A. Bilman, "Extension of Popov absolute stability criterion to nonautonomous systems with delays, International Journal of Control,vol. 73, pp. 1349-1361, 2000.
[2] Y. He and M. Wu, "Absolute stability for multiple delay general Lur-e control systems with multiple nonlinearities, Journal of Computational and Applied Mathematics, vol. 159, pp. 241-248, 2003.
[3] L. Yu, Q.-L. Han, S. Yu, and J. Gao, "Delay-dependent conditions for robust absolute stability of uncertain time-delay systems, in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii USA, 2003, pp.6033-6037.
[4] Y. He, M. Wu, J.-H. She, and G.-P. Liu, "Robust stability for delay Lur-e control systems with multiple nonlinearities, Journal of Computational and Applied Mathematics, vol. 176, pp. 371-380, 2005.
[5] Y.S. Lee, Y.S. Moon, and W.K. Kwon, "Delay-dependent Guaranteed Cost Control for Uncertain State-delay Systems, in Proceeding of the American Control Conference, Arlington, VA, 2001, pp. 3376-3381.
[6] P.G. Park, J.W. Ko, C. Jeong, "Reciprocally convex approach to stability of systems with time-varying delays, Automatica, vol. 47, pp. 235-238, 2011.
[7] Q.L. Han, "Absolute stability of time-delay systems with sector-bounded nonlinearity, Automatica, vol. 41, pp. 2171-2176, 2005.
[8] Y. Cao, and B.T. Cui, "On the absolute stabilization of dynamical-delay systems, Nonlinear Dynamics and Systems Theory 8, vol. 3, pp. 287-298, 2008.
[9] Ben Abdallah, A. Ben Hamed, B. and Chaabane, M. "Absolute Stability and Application to Design of Observer-Based Controller for Nonlinear Time-Delay Systems, Asian Journal of Control 9, vol. 3, pp. 362-371, 2007.
[10] S. Boyd, L.El. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, SIAM, 1994.