Robust Passivity Control for Uncertain Time-Delayed Systems

Abstract:

This paper focuses on the robust passivity synthesis problem for a class of linear time-delayed systems subject to parameter uncertainties. The time delay is assumed to be unknown, and the parameter uncertainties are allowed to appear in all matrices of the model. The aim lies in designing observer-based dynamic controller that render the closed-loop system be strongly robustly stable and strict passive for all admissible uncertainties, independently of time delay. Using a scaling parameterization approach, the problem being considered is transformed into a class of strongly stable and strictly passive control problem for a parameterized system without uncertainties. And then, the controller gain and the observer gain are obtained in terms of a linear matrix inequality. Finally, a numerical example is provided to demonstrate the validity of the proposed approach.

• Periodical: Applied Mechanics and Materials (Volumes 29-32)
• Pages: 2025-2030
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.29-32.2025
• Online since: August 2010
• Authors: Gui Fang Li, Yong Cheng Sun, Sheng Guo Huang
• Keywords: Linear Matrix Inequality (LMI), Observer, Parametric Uncertainty, Passive Control, Time-Delayed Systems

References

[1] L. Dugard and E.I. Verriest: Stability and control of time-delay systems (Springer-Verlag, London, 1998).

[2] M.S. Mahmoud, Y.C. Soh and L. Xie. Observer-based positive real control of uncertain linear systems. Automatica, vol. 35(1999), pp.749-754.

DOI: 10.1016/s0005-1098(98)00216-7

[3] S.I. Niculescu and R. Lozano. On the passivity of linear delay systems. IEEE Trans. Automat. Control, vol. 46(2001), pp.460-464.

DOI: 10.1109/9.911424

[4] A. van der Schaft: 2L -gain and passivity techniques in nonlinear control (Springer-Verlag, London, 1996).