×

A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation. (English) Zbl 1059.93081

Summary: We study observer design for sampled-data nonlinear systems using two approaches: (i) the observer is designed via an approximate discrete-time model of the plant; (ii) the observer is designed based on the continuous-time plant model and then discretized for sampled-data implementation (emulation). We investigate under what conditions, and in what sense, these designs achieve convergence for the unknown exact discrete-time model. We present examples which show that designs that violate our conditions may indeed lead to instability when implemented on the exact model.

MSC:

93C57 Sampled-data control/observation systems
93B07 Observability
Full Text: DOI

References:

[1] Arcak, M., & Nešić, D. (2004). Sampled-data observer design via approximate discrete-time models and emulation. \( Technical Report www.ecse.rpi.edu/homepages/arcak/Dtobs v2.pdf .\); Arcak, M., & Nešić, D. (2004). Sampled-data observer design via approximate discrete-time models and emulation. \( Technical Report www.ecse.rpi.edu/homepages/arcak/Dtobs v2.pdf .\)
[2] Boutayeb, M.; Darouach, M., A reduced-order observer for non-linear discrete-time systems, Systems and Control Letters, 39, 141-151 (2000) · Zbl 0951.93010
[3] Chung, S.-T.; Grizzle, J. W., Sampled-data observer error linearization, Automatica, 26, 6, 997-1007 (1990) · Zbl 0717.93040
[4] Dabroom, A. M.; Khalil, H. K., Output-feedback sampled-data control of nonlinear systems using high-gain observers, IEEE Transactions on Automatic Control, 46, 11, 1712-1725 (2001) · Zbl 1026.93034
[5] Laila, D. S.; Nešić, D.; Teel, A. R., Open and closed loop dissipation inequalities under sampling and controller emulation, European Journal of Control, 8, 2, 109-125 (2002) · Zbl 1293.93388
[6] Nadri, M.; Hammouri, H., Design of a continuous-discrete observer for state-affine systems, Applied Mathematics Letters, 16, 967-974 (2003) · Zbl 1068.93014
[7] Nešić, D., Teel, A. R. (2004). A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models. IEEE Transactions on Automatic Control49; Nešić, D., Teel, A. R. (2004). A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models. IEEE Transactions on Automatic Control49 · Zbl 1365.93281
[8] Nešić, D.; Teel, A. R.; Kokotović, P. V., Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations, Systems and Control Letters, 38, 259-270 (1999) · Zbl 0985.93034
[9] Stuart, A. M.; Humphries, A. R., Dynamical systems and numerical analysis (1996), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0869.65043
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.