Optimal unbiased reduced order filtering for discrete-time descriptor systems via LMI. (English) Zbl 1161.93026
Summary: The reduced order unbiased optimal \(\mathcal H_\infty\) filtering problem for discrete-time descriptor linear systems is considered. Necessary and sufficient conditions for the existence of unbiased causal time invariant filters are obtained. Solutions of the filtering problems are given in terms of Linear Matrix Inequalities (LMIs). Parametrization of all optimal causal unbiased filters is provided. The proposed method generalizes the existing results in the standard case.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93B36 | \(H^\infty\)-control |
| 93C55 | Discrete-time control/observation systems |
Keywords:
reduced order filter; descriptor systems; unbiased filtering; linear matrix inequality (LMI)References:
| [1] | Luenberger, D., Dynamic equations in descriptor form, IEEE Transactions on Automatic Control, 32, 312-321 (1977) · Zbl 0354.93007 |
| [2] | Mills, J.; Goldenberg, A., Force and position control of manipulators during constrained motion tasks, IEEE Transactions on Robotics and Automation, 68, 30-46 (1989) |
| [3] | Dai, L., (Singular Control Systems. Singular Control Systems, Lecture Notes in Control and Information Sciences, vol. 118 (1989), Springer-Verlag: Springer-Verlag New York) · Zbl 0669.93034 |
| [4] | Nikoukhah, R.; Willsky, A.; Levy, B., Kalman filtering and Riccati equations for descriptor systems, IEEE Transactions on Automatic Control, 37, 1325-1342 (1992) · Zbl 0756.93052 |
| [5] | Darouach, M.; Zasadzinski, M.; Mehdi, D., State estimation of stochastic singular linear systems, International Journal of Systems Science, 24, 345-354 (1993) · Zbl 0797.93045 |
| [6] | Darouach, M.; Zasadzinski, M.; Bassong Onana, A., Connection between the 3-block generalized Riccati equation and the standard Riccati equation, IEEE Transactions on Automatic Control, 39, 1755-1758 (1994) · Zbl 0925.93905 |
| [7] | Nikoukhah, R.; Campbell, S.; Delebecque, F., Kalman filtering for general discrete-time systems, IEEE Transactions on Automatic Control, 44, 1829-1839 (1999) · Zbl 0965.93096 |
| [8] | Nagpal, K.; Khargonekar, P., Filtering and smoothing in an \(H_\infty\) setting, IEEE Transactions on Automatic Control, 36, 152-166 (1991) · Zbl 0758.93074 |
| [9] | Darouach, M., On the optimal unbiased functional filtering, IEEE Transactions on Automatic Control, 45, 1374-1379 (2000) · Zbl 0991.93116 |
| [10] | Watson, J.; Grigoriadis, K., Optimal unbiased filtering via linear matrix inequalities, Systems & Control Letters, 35, 111-118 (1998) · Zbl 0909.93069 |
| [11] | Xu, S.; Lam, J., Reduced-order \(H_\infty\) filtering for singular systems, Systems & Control Letters, 56, 48-57 (2007) · Zbl 1120.93321 |
| [12] | Zhang, G.; Xia, Y.; Shi, P., New bounded real lemma for discrete-time singular systems, Automatica, 44, 886-890 (2008) · Zbl 1283.93179 |
| [13] | Rao, C.; Mitra, S., Generalized Inverse of Matrices and Its Applications (1971), Wiley: Wiley New York · Zbl 0236.15004 |
| [14] | Skelton, R.; Iwasaki, T.; Grigoriadis, K., A Unified Algebraic Approach to Linear Control Design (1998), Taylor & Francis: Taylor & Francis London |
| [15] | Iwasaki, T.; Skelton, R., All controllers for the general \(H_\infty\) control problems: LMI existence conditions and state space formulas, Automatica, 30, 1307-1317 (1994) · Zbl 0806.93017 |
| [16] | Xu, S.; Yang, C., Stabilization of discrete-time singular systems: A matrix inequalities approach, Automatica, 35, 1613-1617 (1999) · Zbl 0959.93048 |
| [17] | Darouach, M., Existence and design of functional observers for linear systems, IEEE Transactions on Automatic Control, 45, 940-943 (2000) · Zbl 0972.93008 |
| [18] | O. Malassé, M. Zasadzinski, C. Iung, M. Hayar, M. Darouach, Comparison of robust loop shaping designs: An application to an electromechanical actuator, in: Proc. IEEE Conf. Control & Applications, Glasgow, UK, 1994; O. Malassé, M. Zasadzinski, C. Iung, M. Hayar, M. Darouach, Comparison of robust loop shaping designs: An application to an electromechanical actuator, in: Proc. IEEE Conf. Control & Applications, Glasgow, UK, 1994 |
| [19] | Darouach, M.; Zasadzinski, M.; Bassong Onana, A.; Nowakowski, S., Kalman filtering with unknown inputs via optimal state estimation of singular systems, International Journal of Systems Science, 26, 2015-2028 (1995) · Zbl 0834.93053 |
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