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Global exponential sampled-data observers for nonlinear systems with delayed measurements. (English) Zbl 1277.93051

Summary: This paper presents new results concerning the observer design for certain classes of nonlinear systems with both sampled and delayed measurements. By using a small gain approach we provide sufficient conditions, which involve both the delay and the sampling period, ensuring exponential convergence of the observer system error. The proposed observer is robust with respect to measurement errors and perturbations of the sampling schedule. Moreover, new results on the robust global exponential state predictor design problem are provided, for wide classes of nonlinear systems.

MSC:

93C57 Sampled-data control/observation systems
93B07 Observability
93C10 Nonlinear systems in control theory
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[1] Arcak, M.; Nesic, D., A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation, Automatica, 40, 11, 1931-1938 (2004) · Zbl 1059.93081
[2] Jazwinski, A., Stochastic Processes and Filtering Theory (1970), Academic Press: Academic Press New York · Zbl 0203.50101
[3] Deza, F.; Busvelle, E.; Gauthier, J.; Rakotopora, D., High gain estimation for nonlinear systems, Systems and Control Letters, 18, 4, 295-299 (1992) · Zbl 0779.93018
[4] Gauthier, J.; Hammouri, H.; Othman, S., A simple observer for nonlinear systems applications to bioreactors, IEEE Transactions on Automatic Control, 37, 6, 875-880 (1992) · Zbl 0775.93020
[5] Nadri, M.; Hammouri, H., Design of a continuous-discrete observer for state affine systems, Applied Mathematics Letters, 16, 6, 967-974 (2003) · Zbl 1068.93014
[6] Ahmed-Ali, T.; Postoyan, R.; Lamnabhi-Lagarrigue, F., Continuous-discrete adaptive observers for state affine systems, Automatica, 45, 12, 2986-2990 (2009) · Zbl 1192.93022
[7] Astorga, C.-M.; Othman, N.; Othman, S.; Hammouri, H.; McKenna, T.-F., Nonlinear continuous-discrete observers: applications to emulsion polymerization reactors, Control Engineering Practice, 10, 1, 3-13 (2002)
[8] Nadri, M.; Hammouri, H.; Astorga, C.-M., Observer design for continuous-discrete time state affine systems up to output injection, European Journal of Control, 10, 3, 252-263 (2004) · Zbl 1293.93118
[11] Dacic, D.; Nesic, D., Observer design for linear networked control systems using matrix inequalities, Automatica, 44, 1, 2840-2848 (2008) · Zbl 1152.93314
[12] Heemels, W. P.M. H.; Teel, A. R.; van de Wouw, N.; Nesic, D., Networked control systems with communication constraints: tradeoffs between transmission intervals, delays and performance, IEEE Transactions on Automatic Control, 55, 8, 1781-1796 (2010) · Zbl 1368.93627
[13] Karafyllis, I.; Kravaris, C., From continuous-time design to sampled-data design of observers, IEEE Transactions on Automatic Control, 54, 9, 2169-2174 (2009) · Zbl 1367.93350
[14] Postoyan, R.; Nesic, D., A framework for the observer design for networked control systems, IEEE Transactions on Automatic Control, 57, 5, 1309-1314 (2012) · Zbl 1369.93107
[15] Postoyan, R.; Nesic, D., On emulated nonlinear reduced-order observers for networked control systems, Automatica, 48, 645-652 (2012) · Zbl 1238.93021
[16] Karafyllis, I.; Kravaris, C., Global exponential observers for two classes of nonlinear systems, Systems and Control Letters, 61, 7, 797-806 (2012) · Zbl 1250.93037
[17] Germani, A.; Manes, C.; Pepe, P., A new approach to state observation of nonlinear systems with delayed output, IEEE Transactions on Automatic Control, 47, 1, 96-101 (2002) · Zbl 1364.93371
[19] Ahmed-Ali, T.; Cherrier, E.; Lamnabhi-Lagarrigue, F., Cascade high gain predictors for nonlinear systems with delayed output, IEEE Transactions on Automatic Control, 57, 1, 221-226 (2012) · Zbl 1369.93003
[20] Hespanha, J.; Naghshtabrizi, P.; Xu, Y., A survey of recent results in networked control systems, IEEE Special Issue on Technology of Networked Control Systems, 95, 1, 138-162 (2007)
[23] Rajamani, R., Observers for Lipschitz nonlinear systems, IEEE Transactions on Automatic Control, 43, 3, 397-401 (1998) · Zbl 0905.93009
[24] Angeli, D.; Sontag, E. D., Forward completeness, unbounded observability and their Lyapunov characterizations, Systems and Control Letters, 38, 4-5, 209-217 (1999) · Zbl 0986.93036
[25] Karafyllis, I.; Jiang, Zhong-Ping, (Stability and Stabilization of Nonlinear Systems. Stability and Stabilization of Nonlinear Systems, Communications and Control Engineering (2011), Springer-Verlag: Springer-Verlag London) · Zbl 1243.93004
[26] Karafyllis, I.; Krstic, M., Nonlinear stabilization under sampled and delayed measurements, and with inputs subject to delay and zero-order hold, IEEE Transactions on Automatic Control, 57, 5, 1141-1154 (2012) · Zbl 1369.93491
[28] Krstic, M., Delay Compensation for Nonlinear, Adaptive, and PDE Systems (2009), Birkhäuser: Birkhäuser Boston · Zbl 1181.93003
[29] Krstic, M., Input delay compensation for forward complete and strict-feedforward nonlinear systems, IEEE Transactions on Automatic Control, 55, 2, 287-303 (2010) · Zbl 1368.93546
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