Observer design for LTD systems and bounded unknown inputs using sliding modes

https://doi.org/10.58571/CNCA.AMCA.2025.023

Resumen: This paper investigates the design of an observer for linear systems with commensurate delays affected by bounded unknown inputs, assuming that the system is observable in the presence of such inputs. The observer proposed by Hou is employed, as well as information from the system output and its derivatives, which are approximated using the high-order Levant's differenciator, to enable fnite-time reconstruction of the system trajectories.

¿Cómo citar?

Pérez Mendieta, G., Bejarano Rodríguez, F. & Dávila Montoya, J. (2025). Observer design for LTD systems and bounded unknown inputs using sliding modes. Memorias del Congreso Nacional de Control Automático 2025, pp. 132-137. https://doi.org/10.58571/CNCA.AMCA.2025.023

Palabras clave

Linear systems, Time-delay, Observers, Sliding mode, Bounded disturbances.

• Bejarano, F.J. and Fridman, L. (2010). High order sliding mode observer for linear systems with unbounded unknown inputs. International Journal of Control, 83(9), 1920{1929. doi:10.1080/00207179.2010.501386. URL https://doi.org/10.1080/ 00207179.2010.501386.
• Bejarano, F.J., Fridman, L., and Poznyak, A. (2009). Unknown Input and State Estimation for Unobservable Systems. SIAM Journal on Control and Optimization, 48(2), 1155{1178. doi:10.1137/070700322. URL https://doi.org/10.1137/070700322.
• Bejarano, F.J. and Zheng, G. (2014). Observability of linear systems with commensurate delays  and unknown inputs. Automatica, 50(8), 2077{2083. doi:10.1016/j.automatica.2014.05.032. URL https://doi.org/10.1016/j.automatica.2014.05.032.
• Bejarano, F.J. and Zheng, G. (2021). Observability and observer design of time-delay linear systems with unknown inputs. doi:10.1016/b978-0-12-820599- 0.00011-2. URL https://doi.org/10.1016/b978-0-12-820599-0.00011-2.
• Conte, G., Perdon, A., and Guidone-Peroli, G. (2003). Unknown input observers for linear delay systems: a geometric approach. In 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), volume 6, 6054{6059 Vol.6. doi: 10.1109/CDC.2003.1272211.
• Fattouh, A., Sename, O., and Dion, J.M. (1999). An unknown input observer design for linear time-delay systems. Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 4, 4222{4227 vol.4. URL  https://api.semanticscholar.org/CorpusID:6958859.
• Fridman, L., Levant, A., and Davila, J. (2007). Observation of linear systems with unknown inputs via high-order sliding-modes. International Journal of Systems Science, 38(10), 773{791. doi:10.1080/00207720701409538. URL https://doi.org/10.1080/00207720701409538.
• Hautus, M. (1983). Strong detectability and observers. Linear Algebra and its Applications, 50, 353{368. doi:10.1016/0024-3795(83)90061-7. URL https://doi.org/10.1016/ 0024-3795(83)90061-7.
• Hou, M., Zitek, P., and Patton, R. (2002). An observer design for linear time-delay systems. IEEE Transactions on Automatic Control, 47(1), 121{125. doi:10.1109/9.981730. URL https://doi.org/10.1109/9.981730.
• Kailath, T. (1980). Linear systems. URL https://openlibrary.org/books/OL4411368M/Linear systems.
• Levant, A. (2003). Higher-order sliding modes, di_erentiation and output-feedback control. International Journal of Control, 76(9-10), 924{941. doi:10.1080/0020717031000099029. URL https://doi.org/ 10.1080/0020717031000099029.
• Molinari, B. (1976). A strong controllability and observability in linear multivariable control. IEEE Transactions on Automatic Control, 21(5), 761{764. doi:10.1109/tac.1976.1101364. URL https://doi.org/10.1109/tac.1976.1101364.
• Trentelman, H.L., Stoorvogel, A.A., and Hautus, M. (2001). Control Theory for Linear Systems. doi:10.1007/978-1-4471-0339-4. URL https://doi.org/10.1007/ 978-1-4471-0339-4.
• Zheng, G., Bejarano, F.J., Perruquetti, W., and Richard, J.P. (2015). Unknown input observer for linear time-delay systems.  Automatica, 61, 35{43. doi:10.1016/j.automatica.2015.07.029. URL https://doi.org/10.1016/j.automatica.2015.07.029.