Sliding-mode observers for systems with unknown inputs: a high-gain approach. (English) Zbl 1205.93028

Summary: Sliding-mode observers can be constructed for systems with unknown inputs if the so-called observer matching condition is satisfied. However, most systems do not satisfy this condition. To construct sliding-mode observers for systems that do not satisfy the observer matching condition, auxiliary outputs are generated using high-gain approximate differentiators and then employed in the design of sliding-mode observers. The state estimation error of the proposed high-gain approximate differentiator based sliding-mode observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. Finally, the unknown input reconstruction using the proposed observer is analyzed and then illustrated with a numerical example.


93B12 Variable structure systems
93B07 Observability
Full Text: DOI


[1] Bartle, R.G., The elements of integration, (1966), John Wiley and Sons New York, NY · Zbl 0146.28201
[2] Chen, J.; Patton, R., Robust model-based fault diagnosis for dynamical systems, (1999), Kluwer Academic Publishers Norwell, Massachusetts · Zbl 0920.93001
[3] Corless, M.; Tu, J., State and input estimation for a class of uncertain systems, Automatica, 34, 6, 757-764, (1998) · Zbl 0932.93008
[4] Darouach, M.; Zasadzinski, M.; Xu, S., Full-order observers for linear systems with unknown inputs, IEEE transactions on automatic control, 39, 3, 606-609, (1994) · Zbl 0813.93015
[5] Edwards, C.; Spurgeon, S.K., Sliding mode control: theory and applications, (1998), Taylor and Francis Group London, UK
[6] Edwards, C.; Spurgeon, S.K.; Patton, R.J., Sliding mode observers for fault detection and isolation, Automatica, 36, 541-553, (2000) · Zbl 0968.93502
[7] Esfandiari, F.; Khalil, H.K., Output feedback stabilization of fully linearizable systems, International journal of control, 56, 1007-1037, (1992) · Zbl 0762.93069
[8] Floquet, T.; Barbot, J.P., A canonical form for the design of unknown input sliding mode observers, () · Zbl 1128.93311
[9] Floquet, T.; Edwards, C.; Spurgeon, S.K., On sliding mode observers for systems with unknown inputs, International journal of adaptive control and signal processing, 21, 638-656, (2007) · Zbl 1128.93008
[10] Hou, M.; Müller, P., Design of observers for linear systems with unknown inputs, IEEE transactions on automatic control, 37, 6, 871-875, (1992) · Zbl 0775.93021
[11] Hui, S.; Żak, S.H., Observer design for systems with unknown inputs, International journal of applied mathematics and computer science, 15, 4, 431-446, (2005) · Zbl 1127.93018
[12] Khalil, H.K., High gain observers in nonlinear feedback control, () · Zbl 1380.93002
[13] Luenberger, D.G., Observers for multivariable systems, IEEE transactions on automatic control, AC-11, 2, 190-197, (1966)
[14] Mahmoud, N.A.; Khalil, H.K., Asymptotic regulation of minimum phase nonlinear systems using output feedback, IEEE transactions on automatic control, 41, 10, 1402-1412, (1996) · Zbl 0869.93021
[15] Walcott, B.; Żak, S.H., State observation of nonlinear uncertain dynamical systems, IEEE transactions on automatic control, 32, 2, 166-170, (1987) · Zbl 0618.93019
[16] Żak, S.H.; Walcott, B., State observation of nonlinear control systems via the method of Lyapunov, (), 333-350
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.