H<inf>∞</inf> observer design for uncertain nonlinear discrete-time systems with time-delay: LMI optimization approach

Sayyaddelshad, Saleh; S. Delshad, Iman; Gustafsson, Thomas

Abstract

Copyright © 2014 John Wiley & Sons, Ltd. We present a robust H∞ observer for a class of nonlinear discrete-time systems. The class under study includes an unknown time-varying delay limited by upper and lower bounds, as well as time-varying parametric uncertainties. We design a nonlinear H∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time-varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi-objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples.

Citation

Sayyaddelshad, S., S. Delshad, I., & Gustafsson, T. (2015). H<inf>∞</inf> observer design for uncertain nonlinear discrete-time systems with time-delay: LMI optimization approach. International Journal of Robust and Nonlinear Control, 25(10), 1514-1527. https://doi.org/10.1002/rnc.3155

• Journal Article Type: Article
• Acceptance Date: Jan 9, 2014
• Online Publication Date: Mar 3, 2014
• Publication Date: Jan 1, 2015
• Journal: International Journal of Robust and Nonlinear Control
• Print ISSN: 1049-8923
• Electronic ISSN: 1099-1239
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 10
• Pages: 1514-1527
• DOI: https://doi.org/10.1002/rnc.3155
• Keywords: discrete-time systems, robust H-infinity observer, nonlinear systems, delay systems, linear matrixinequalities
• Public URL: https://uwe-repository.worktribe.com/output/831317
• Publisher URL: http://dx.doi.org/10.1002/rnc.3155
• Related Public URLs: http://onlinelibrary.wiley.com/doi/10.1002/rnc.3155/abstract