René Meléndez-Pérez | Universidad Nacional Autónoma de México |
Jaime A. Moreno | Universidad Nacional Autónoma de México |
Leonid Fridman | Universidad Nacional Autónoma de México |
https://doi.org/10.58571/CNCA.AMCA.2022.054
Resumen: In this article, a family of state observers with bl- homogeneous properties is proposed for a class of linear systems with time-varying coefficients, in presence of an unknown input and with an arbitrary relative degree. The proposed observers converge globally and at least asymptotically to the true states for systems that satisfy the structural property of strong observability. With an adequate selection of gains and parameters the convergence is global and theoretically exact, in finite time or even more, in fixed time.

¿Cómo citar?
Meléndez-Pérez, R., Moreno, J. & Fridman, L. Bl-homogeneous sliding-mode observers for SISO linear time-varying systems with unknown input. Memorias del Congreso Nacional de Control Automático, pp. 294-299, 2022. https://doi.org/10.58571/CNCA.AMCA.2022.054
Palabras clave
Control Discontinuo (modos deslizantes); Control de Sistemas No Lineales; Control Robusto
Referencias
- Andrieu, V., Praly, L., and Astolfi, A. (2008). Homogeneous approximation, recursive observer design, and output feedback. SIAM Journal on Control and Optimization, 47(4), 1814–1850.
- Barbot, J.P., Djemai, M., and Boukhobza, T. (2002). Sliding mode observers. In Sliding Mode Control In Engineering, Automation and Control Engineering.
- Dávila, J., Tranninger, M., and Fridman, L. (2022). Finite-time state observer for a class of linear timevarying systems with unknown inputs. IEEE Transactions on Automatic Control, 67(6), 3149–3156.
- Filippov, A.F. (1988). Differential Equations with Discontinuous Righthand Side, volume 18. Springer Science & Business Media.
- Galvan, R., Fridman, L., and Davila, J. (2016). Highorder sliding-mode observer for linear time varying systems with unknown inputs. International Journal of Robust and Nonlinear Control, 27.
- Hautus, M. (1983). Strong detectability and observers. Linear Algebra and its Applications, 50, 353–368.
- Kratz, W. (1995). Characterization of strong observability and construction of an observer. Linear Algebra and its Applications, 221, 31–40.
- Kratz, W. and Liebscher, D. (1998). A local characterization of observability. Linear Algebra and its Applications, 269(1), 115–137.
- Lugo Segura, R. (2014). Observador para sistemas LTV con entradas desconocidas basado en modos deslizantes de orden superior. Tesis de maestría, UNAM.
- Menold, P., Findeisen, R., and Allg¨ower, F. (2004). Finite time convergent observers for nonlinear systems. In Proceedings of the IEEE Conference on Decision and Control, volume 6, 5673 – 5678 Vol.6.
- Molinari, B. (1976). A strong controllability and observability in linear multivariable control. IEEE Transactions on Automatic Control, 21(5), 761–764.
- Moreno, J.A. (2021). Arbitrary-order fixed-time differentiators. IEEE Transactions on Automatic Control, 67(3), 1543–1549.
- Silverman, L. (1969). Inversion of multivariable linear systems. IEEE Transactions on Automatic Control, 14(3), 270–276.
- Spurgeon, S.K. (2008). Sliding mode observers: a survey. International Journal of Systems Science, 39(8).
- Trumpf, J. (2007). Observers for linear time-varying systems. Linear Algebra and its Applications, 425(2).
- Yan, X.G. and Edwards, C. (2007). Nonlinear robust fault reconstruction and estimation using a sliding mode observer. Automatica, 43(9), 1605 – 1614.
- Zhang, Q. and Clavel, A. (2001). Adaptive observer with exponential forgetting factor for linear time varying systems. In Proceedings of the 40th IEEE Conference on Decision and Control, volume 4, 3886–3891 vol.4.