zbMATH — the first resource for mathematics

Design of observers for a class of discrete-time uncertain nonlinear systems with time delay. (English) Zbl 1073.93007
State observers for a class of discrete-time nonlinear systems with Lipschitz coefficients and with uncertainties are designed. Conditions for guaranteeing the asymptotic stability of the error dynamics are presented in terms of an LMI. The solvability conditions are delay-independent.

93B07 Observability
93B51 Design techniques (robust design, computer-aided design, etc.)
93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
15A39 Linear inequalities of matrices
93D20 Asymptotic stability in control theory
Full Text: DOI
[1] Chen, C.-T., Linear system theory and design, (1984), Holt Rinehart & Winston New York
[2] O’Reilly, J., Observers for linear systems, (1983), Academic Press New York · Zbl 0513.93001
[3] Zhang, S.-Y., Function observer and state feedback, Int. J. control, 46, 1295-1305, (1987) · Zbl 0623.93010
[4] Barmish, B.R.; Galimidi, A.R., Robustness of luenberger observerslinear systems stabilized via nonlinear control, Automatica, 22, 413-423, (1986) · Zbl 0598.93045
[5] Chen, J.; Patton, R.J.; Zhang, H.Y., Design of unknown input observers and robust fault detection filter, Int. J. control, 63, 85-105, (1996) · Zbl 0844.93020
[6] X. Ding, P.M. Frank, L. Guo, Robust observer design via factorization, in: Proceedings of the 29th Conference on Decision Control, Honolulu, HI, USA, 1990, pp. 3623-3628.
[7] Gorecki, H.S.; Fuska, P.; Grabowski, S.; Korytowski, A., Analysis and synthesis of time delay systems, (1989), Wiley New York · Zbl 0695.93002
[8] Hale, J.K., Theory of functional differential equations, (1977), Springer New York · Zbl 0425.34048
[9] Trinh, H.; Aldeen, M., A memoryless state observer for discrete time-delay systems, IEEE trans. autom. control, 42, 1572-1577, (1997) · Zbl 1034.93508
[10] Yao, Y.X.; Zhang, Y.M.; Kovacevic, R., Functional observer and state feedback for input time-delay systems, Int. J. control, 66, 603-617, (1997) · Zbl 0873.93015
[11] Krener, A.J.; Respondek, W., Nonlinear observers with linearizable error dynamics, SIAM J. control optim., 23, 179-216, (1985) · Zbl 0569.93035
[12] Krstić, M.; Kanellakopoulos, I.; Kokotovic, P.V., Nonlinear and adaptive control design, (1995), Wiley New York · Zbl 0763.93043
[13] Rajamani, R., Observers for Lipschitz nonlinear systems, IEEE trans. autom. control, 43, 397-401, (1998) · Zbl 0905.93009
[14] E. Yaz, W. Na Nacara, Nonlinear estimation by covariance assignment, in: Preprints of the 12th IFAC World Congress, Vol. 6, Sydney, Australia, 1993, pp. 87-90.
[15] Wang, Z.; Unbehauen, H., A class of nonlinear observers for discrete-time systems with parametric uncertainty, Int. J. syst. sci., 31, 19-26, (2000) · Zbl 1080.93634
[16] Khargonekar, P.P.; Petersen, I.R.; Zhou, K., Robust stabilization of uncertain linear systemsquadratic stabilizability and H∞ control theory, IEEE trans. autom. control, 35, 356-361, (1990) · Zbl 0707.93060
[17] Xie, L.; Soh, Y.C., Robust Kalman filtering for uncertain systems, Syst. control lett., 22, 123-129, (1994) · Zbl 0792.93118
[18] Xu, S.; Lam, J.; Yang, C., Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay, Syst. control lett., 43, 77-84, (2001) · Zbl 0974.93052
[19] Wang, Y.; Xie, L.; de Souza, C.E., Robust control of a class of uncertain nonlinear systems, Syst. control lett., 19, 139-149, (1992) · Zbl 0765.93015
[20] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequalities in system and control theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, PA, 1994. · Zbl 0816.93004
[21] Cao, Y.-Y.; Sun, Y.-X.; Lam, J., Delay-dependent robust H∞ control for uncertain systems with time-varying delays, IEE proc.-control theory appl., 145, 338-344, (1998)
[22] Li, X.; de Souza, C.E., Delay-dependent robust stability and stabilization of uncertain linear delay systemsa linear matrix inequality approach, IEEE trans. autom. control, 42, 1144-1148, (1997) · Zbl 0889.93050
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.