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.

• 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