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State estimators for uncertain linear systems with different disturbance/noise using quadratic boundedness. (English) Zbl 1244.93156

Summary: This paper designs state estimators for uncertain linear systems with polytopic description, different state disturbance, and measurement noise. Necessary and sufficient stability conditions are derived followed with the upper bounding sequences on the estimation error. All the conditions can be expressed in the form of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the approach.

MSC:

93E10 Estimation and detection in stochastic control theory
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[1] J. H. Kim and J. H. Oh, “Robust state estimator of stochastic linear systems with unknown disturbances,” IEE Proceedings, vol. 147, no. 2, pp. 224-228, 2000. · doi:10.1049/ip-cta:20000174
[2] M. Fu and C. E. de Souza, “State estimation for linear discrete-time systems using quantized measurements,” Automatica, vol. 45, no. 12, pp. 2937-2945, 2009. · Zbl 1192.93115 · doi:10.1016/j.automatica.2009.09.033
[3] B. Boulkroune, M. Darouach, and M. Zasadzinski, “Moving horizon state estimation for linear discrete-time singular systems,” IET Control Theory and Applications, vol. 4, no. 3, pp. 339-350, 2010. · doi:10.1049/iet-cta.2008.0280
[4] S. Pillosu, A. Pisano, and E. Usai1, “Decentralised state estimation for linear systems with unknown inputs: a consensus-based approach,” IET Control Theory & Applications, vol. 5, no. 3, pp. 498-506, 2011. · doi:10.1049/iet-cta.2010.0086
[5] A. Alessandri, M. Baglietto, and G. Battistelli, “Design of state estimators for uncertain linear systems using quadratic boundedness,” Automatica, vol. 42, no. 3, pp. 497-502, 2006. · Zbl 1123.93052 · doi:10.1016/j.automatica.2005.10.013
[6] M. L. Brockman and M. Corless, “Quadratic boundedness of nonlinear dynamical systems,” in Proceedings of the 34th IEEE Conference on Decision and Control, pp. 504-509, New Orleans, La, USA, December 1995.
[7] M. L. Brockman and M. Corless, “Quadratic boundedness of nominally linear systems,” International Journal of Control, vol. 71, no. 6, pp. 1105-1117, 1998. · Zbl 0981.93071 · doi:10.1080/002071798221506
[8] M. L. Ni and M. J. Er, “Design of linear uncertain systems guaranteeing quadratic boundedness,” in Proceedings of the Americal Control Conference, pp. 3832-3836, Chicago, Ill, USA, June 2000.
[9] B. Ding and L. Xie, “Dynamic output feedback robust model predictive control with guaranteed quadratic boundedness,” in Proceedings of the 48th IEEE Conference on Decision and Control (CDC/CCC ’09), pp. 8034-8039, Shanghai, China, December 2009. · doi:10.1109/CDC.2009.5399784
[10] B. Ding, “Quadratic boundedness via dynamic output feedback for constrained nonlinear systems in Takagi-Sugeno’s form,” Automatica, vol. 45, no. 9, pp. 2093-2098, 2009. · Zbl 1175.93121 · doi:10.1016/j.automatica.2009.05.017
[11] B. Ding, “Dynamic output feedback predictive control for nonlinear systems represented by a takagi-sugeno model,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 5, pp. 831-843, 2011.
[12] B. Ding, Y. Xi, M. T. Cychowski, and T. O’Mahony, “A synthesis approach for output feedback robust constrained model predictive control,” Automatica, vol. 44, no. 1, pp. 258-264, 2008. · Zbl 1138.93340 · doi:10.1016/j.automatica.2007.04.005
[13] B. Ding, “New formulation of dynamic output feedback robust model predictive control with guaranteed quadratic boundedness,” in Proceedings of the 30th Chinese Control Conference, pp. 3346-3351, Yantai, China, July 2011.
[14] A. Alessandri, M. Baglietto, and G. Battistelli, “On estimation error bounds for receding-horizon filters using quadratic boundedness,” IEEE Transactions on Automatic Control, vol. 49, no. 8, pp. 1350-1355, 2004. · Zbl 1365.93495 · doi:10.1109/TAC.2004.832652
[15] M. Chilali and P. Gahinet, “H\infty design with pole placement constraints: an LMI approach,” IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 358-367, 1996. · Zbl 0857.93048 · doi:10.1109/9.486637
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