Abstract
This paper presents a state observer for linear systems and Lipschitz nonlinear systems with delayed output measurements, which are affected by a known and bounded time-varying delay. The structure of the proposed observer is based on a proportional-integral term, which allows to compensate the time-varying delay. The observer gain depends on the maximum bounded delay. This gain is computed by a Linear Matrix Inequality (LMI) approach. The observer exhibits good performance for state estimation of the system despite the presence of significantly long delay. A Lyapunov-Krasovskii functional is used to prove the asymptotical convergence to zero of the observation error. This observer is applied to the case of systems with time-varying delay whose dynamic is described by a piecewise differentiable function. Examples and numerical simulations are provided in order to support the validity of the main results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. V. Assche, T. Ahmed–Ali, C.A.B. Hann, and F. Lamnabhi–Lagarrigue, “High gain observer design for nonlinear systems with time varying delayed measurements,” Proc. of the 18thWorld Congress, pp. 692–696, Aug. 2011.
N. Bekiaris–Liberis and M. Krstic, “Compensation of State–Dependent Input Delay for Nonlinear Systems,” IEEE Trans. on Automatic Control, vol. 58, no. 2, pp. 275–289, Feb. 2013.
G. Besancon, D. Georges, and Z. Benayache, “Asymptotic state prediction for continuous–time systems with delayed input and application to control,” Proc. of European Control Conference, pp. 1786.1791, Kos, Greece, July 2007.
F. Cacace, A. Germani and C. Manes, “An observer for a class of nonlinear systems with time–varying observation delay,” Systems & Control Letters, vol. 59, no. 5, pp. 305–312, May 2010.
M. Darouach, “Linear functional observers for systems with delays in state variables,” IEEE Trans. on Automatic Control, vol. 46, no. 3, pp. 491–496, Mar. 2001.
A. Germani, C. Manes, and P. Pepe, “A new approach to state observation of nonlinear systems with delayed output,” IEEE Trans. on Automatic Control, vol. 47, no. 1, pp. 96–101, Aug. 2002.
R. Houimli, N. Bedioui, and M. Besbes, “An improved polytopic adaptive LPV observer design under actuator fault,” International Journal of Control, Automation and Systems, vol. 16, no. 1, pp. 168–180, Mar. 2018.
N. Kazantzis and R. A. Wright, “Nonlinear observer design in the presence of delayed output measurements,” Systems & Control Letters, vol. 54, no. 9, pp. 877–886, Sep. 2005.
M. Kazerooni, A. Khayatian, and A. A. Safavi, “Robust delay dependent fault estimation for a class of interconnected nonlinear time delay systems,” International Journal of Control, Automation, and Systems, vol. 14, no. 2, pp.569–578, April 2016.
J. Lei and H.–K. Khalil, “High–gain–predictor–based output feedback control for time–delay nonlinear systems,” Automatica, vol. 71, no. 1, pp. 324333, Sep. 2016.
J. Lu, C. Feng, S. Xu, and Y. Chu, “Observer design for a class of uncertain state–delayed nonlinear systems,” International Journal of Control, Automation, and Systems, vol. 4, no. 4, pp. 448–455, Aug. 2006.
S. Mobayen, “Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback,” Nonlinear Dynamics, vol. 76, no. 1, pp 827–838, Dec. 2013.
S. Mondie and W. Michiels, “Finite spectrum assignment of unstable time–delay systems with a safe implementation,” IEEE Trans. on Automatic Control, vol. 48, no. 12, pp. 2207–2212, Dec. 2003.
S. Santra, H. R. Karimi, R. Sakthivel, and S. Marshal Anthoni, “Dissipative based adaptive reliable sampleddata control of time–varying delay Systems,” International Journal of Control, Automation, and Systems, vol. 14, no. 1, pp. 39–50, Feb. 2016.
K. Subbarao and P. C. Muralidhar, “A state observer for LTI systems with delayed outputs: time–varying delay,” Proc. of American Control Conference, pp. 3029.3033, Seattle, USA, June 2008.
Y. Wang, D. Zhao, Y. Li, and S. X. Ding, “Unbiased minimum variance fault and state estimation for linear discrete time–varying two–dimensional systems,” IEEE Trans. on Automatic Control, vol. 62, no. 10, pp. 5463–5469, April 2017.
D. Zhao, D. Shen, and Y. Wang, “Fault diagnosis and compensation for two–dimensional discrete time systems with sensor faults and time–varying delays,” International Journal of Robust and Nonlinear Control, vol. 27, no. 16, pp. 3296–3320, Dec. 2016.
Y. Zhao, J. Tao, and N.–Z. Shi, “A note on observer design for one–sided Lipschitz nonlinear systems,” Systems & Control Letters, vol. 59, no. 1, pp. 66–71, Jan. 2010.
G. Zheng and F.–J. Bejaranoc, “Observer design for linear singular time–delay systems,” Automatica, vol 80, no. 1, pp. 1–9, June 2017.
M. Zhong, D. Zhou, and S. X. Ding, “On designing H¥ fault detection filter for linear discrete time–varying systems,” IEEE Trans. on Automatic Control, vol. 55, no. 7, pp. 1689–1695, July 2010.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Nam H. Jo under the direction of Editor PooGyeon Park.
Boubekeur Targui received the Ph.D. degrees in control engineering from the University of Claude Bernard Lyon I, Lyon, France, in 2000. Since 2002, he has held a position of Associate Professor in University de Caen, France. His current research interests are in nonlinear observers and automatic control.
Omar Hernandez-Gonzalez received his M.Sc. degree in electronic engineering from CENIDET, México, in 2008, and the Ph.D. degree in automatic from the University of Caen Normandie, France, in 2017. Since 2008, he has held a position of Professor in the Technological Institute of México / Coatzacoalcos (ITESCO). His research interests include the nonlinear observers.
Carlos-Manuel Astorga-Zaragoza received the Ph.D. degree in process engineering from the University of Claude Bernard Lyon 1, France, in 2001. Since 1993, he has held teaching and research positions at the CENIDET, where he mainly works on observers and fault detection systems for energy conversion processes.
Gerardo-Vicente Guerrero-Ramírez received the Ph.D. degree in Engineering from the Universidad Nacional Autónoma de México (UNAM), México, in 2001. He is currently a professor of department of electronic engineering at the Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET).
María-Eusebia Guerrero-Sánchez received the Ph.D. degree in electronic engineering from the Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET), México, in 2017. She is currently a Professor of the Technological Institute of México / Coatzacoalcos (ITESCO). Her research interests are focused on passivity-based control, nonlinear control, and UAV.
Rights and permissions
About this article
Cite this article
Targui, B., Hernández-González, O., Astorga-Zaragoza, CM. et al. A New Observer Design for Systems in Presence of Time-varying Delayed Output Measurements. Int. J. Control Autom. Syst. 17, 117–125 (2019). https://doi.org/10.1007/s12555-017-0224-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-017-0224-x