Robust filtering with guaranteed energy-to-peak performance – \({\mathcal LMI}\) approach. (English) Zbl 0953.93067
The paper investigates the robust filtering problem with guaranteed energy-to-peak performance for linear systems with convex bounded uncertainties through a linear matrix inequalities (\(\mathcal{LMI}\)) approach. Both continuous- and dicrete-time systems are considered. Necessary and sufficient conditions are obtained for full order filtering allowing the problem to be solved through convex optimization procedures.
Reviewer: Georgi Boshnakov (Manchester /UK)
References:
| [1] | Albert, A., Conditions for positive and nonnegative definiteness in terms of pseudoinverses, SIAM Journal on Applied Mathematics, 17, 2, 434-440 (1969) · Zbl 0265.15002 |
| [2] | Bernstein, D. S., Some open problems in matrix theory arising in linear systems and control, Linear Algebra and its Applications, 162, 409-432 (1992) · Zbl 0765.93026 |
| [3] | Chilali, M.; Gahinet, P., \(H∞\) design with pole placement constraints: An \(LMI\) Approach, IEEE Transactions on Automatic Control, 41, 358-367 (1996) · Zbl 0857.93048 |
| [4] | Fialho, I. J., & Georgiou, T. T. (1995). On the \(L1\) norm of uncertain linear systems. Proceedings of the 1995 American control conference, Seattle, WA, USA (pp. 939-943).; Fialho, I. J., & Georgiou, T. T. (1995). On the \(L1\) norm of uncertain linear systems. Proceedings of the 1995 American control conference, Seattle, WA, USA (pp. 939-943). |
| [5] | Geromel, J. C., Bernussou, J., Garcia, G., & de Oliveira, M. C. (1998). \(H2\) and \(H∞\) robust filtering for discrete-time linear systems. Proceedings of the 37th IEEE Conference on decision and control, Tampa, FL, USA (pp. 632-637).; Geromel, J. C., Bernussou, J., Garcia, G., & de Oliveira, M. C. (1998). \(H2\) and \(H∞\) robust filtering for discrete-time linear systems. Proceedings of the 37th IEEE Conference on decision and control, Tampa, FL, USA (pp. 632-637). |
| [6] | Geromel, J. C., & de Oliveira, M. C. (1998). \(H2\) and \(H∞\) robust filtering for convex bounded uncertain systems. Proceedings of the 37th IEEE conference on decision and control, Tampa, FL, USA (pp. 146-151).; Geromel, J. C., & de Oliveira, M. C. (1998). \(H2\) and \(H∞\) robust filtering for convex bounded uncertain systems. Proceedings of the 37th IEEE conference on decision and control, Tampa, FL, USA (pp. 146-151). |
| [7] | Grigoriadis, K. M., \(L2\) and \(L2-L∞\) model reduction via linear matrix inequalities, International Journal of Control, 68, 3, 485-498 (1997) · Zbl 0890.93013 |
| [8] | Grigoriadis, K. M.; Watson, J. T., Reduced-order \(H∞\) and \(L2-L∞\) filtering via linear matrix inequalities, IEEE Transactions on Aerospace and Electronic Systems, 33, 4, 1326-1338 (1997) |
| [9] | Kalman, R. E., A new approach to linear filtering and prediction problems, Transactions of ASME — Journal of Basic Engineering, 82, 35-45 (1960) |
| [10] | Khargonekar, P. P.; Rotea, M. A.; Baeyens, E., Mixed \(H2/H∞\) filtering, International Journal of Robust and Nonlinear Control, 6, 4, 313-330 (1996) · Zbl 0849.93063 |
| [11] | Li, H.; Fu, M., A linear matrix inequality approach to robust \(H∞\) filtering, IEEE Transactions on Signal Processing, 45, 9, 2338-2350 (1997) |
| [12] | Nagpal, K.; Abedor, J.; Poolla, K., A linear matrix inequality approach to peak-to-peak gain minimization, International Journal of Robust and Nonlinear Control, 6, 899-927 (1996) · Zbl 0862.93028 |
| [13] | Palhares, R. M.; Peres, P. L.D., Optimal filtering schemes for linear discrete-time systems — an \(LMI\) approach, International Journal of Systems Science, 29, 6, 587-593 (1998) |
| [14] | Palhares, R. M.; Peres, P. L.D., Robust \(H∞\) filtering design with pole placement constraint via \(LMI\) s, Journal of Optimization Theory and Applications, 102, 2, 239-261 (1999) · Zbl 0941.93018 |
| [15] | Palhares, R. M.; Takahashi, R. H.C.; Peres, P. L.D., \(H∞\) and \(H2\) guaranteed costs computation for uncertain linear systems, International Journal of Systems Science, 28, 2, 183-188 (1997) · Zbl 0922.93014 |
| [16] | Park, P.; Kailath, T., \(H∞\) filtering via convex optimization, International Journal of Control, 66, 1, 15-22 (1997) · Zbl 0870.93041 |
| [17] | Peres, P. L.D.; Geromel, J. C.; Bernussou, J., Quadratic stabilizability of linear uncertain systems in convex-bounded domains, Automatica, 29, 2, 491-493 (1993) · Zbl 0772.93063 |
| [18] | Rauch, H. E.; Tung, F.; Striebel, C. T., Maximum likelihood estimates of linear dynamic systems, AIAA Journal, 3, 1445-1450 (1965) |
| [19] | Rotea, M. A., The generalized \(H2\) control problem, Automatica, 29, 2, 373-385 (1993) · Zbl 0772.93027 |
| [20] | Scherer, C. (1995). Mixed \(H2/H∞\) control. In: A. Isidori, Trends in control (pp. 173-216) Berlin: Springer.; Scherer, C. (1995). Mixed \(H2/H∞\) control. In: A. Isidori, Trends in control (pp. 173-216) Berlin: Springer. |
| [21] | Scherer, C.; Gahinet, P.; Chilali, M., Multiobjective output-feedback control via \(LMI\) optimization, IEEE Transactions on Automatic Control, 42, 7, 896-911 (1997) · Zbl 0883.93024 |
| [22] | Shaked, U.; de Souza, C. E., Robust minimum variance filtering, IEEE Transactions on Signal Processing, 43, 11, 2474-2483 (1994) |
| [23] | Skelton, R., Iwasaki, T., & Grigoriadis, K. (1997). A unified algebraic approach to linear control designs. London: Taylor & Francis.; Skelton, R., Iwasaki, T., & Grigoriadis, K. (1997). A unified algebraic approach to linear control designs. London: Taylor & Francis. |
| [24] | Takaba, K.; Katayama, T., Discrete-time \(H∞\) algebraic Riccati equation and paremetrization of all \(H∞\) filters, International Journal of Control, 64, 6, 1129-1149 (1996) · Zbl 0862.93057 |
| [25] | Vincent, T., Abedor, J., Nagpal, K., & Khargonekar, R. P. (1996). Discrete-time estimators with guaranteed peak-to-peak performance. Proceedings of the 13th IFAC Triennial World Congress, San Francisco, CA, USA (pp. 43-48).; Vincent, T., Abedor, J., Nagpal, K., & Khargonekar, R. P. (1996). Discrete-time estimators with guaranteed peak-to-peak performance. Proceedings of the 13th IFAC Triennial World Congress, San Francisco, CA, USA (pp. 43-48). |
| [26] | Voulgaris, P. G., Optimal \(ℓ_∞\) to \(ℓ_∞\) estimation for periodic systems, IEEE Transactions on Automatic Control, 41, 9, 1392-1396 (1996) · Zbl 0858.93042 |
| [27] | Watson, J. T., & Grigoriadis, K. M. (1997). Optimal unbiased filtering via linear matrix inequalities. Proceedings of the 1997 American control conference, Albuquerque, NM, USA (pp. 2825-2829).; Watson, J. T., & Grigoriadis, K. M. (1997). Optimal unbiased filtering via linear matrix inequalities. Proceedings of the 1997 American control conference, Albuquerque, NM, USA (pp. 2825-2829). |
| [28] | Wilson, D. A., Convolution and Hankel operator norms for linear systems, IEEE Transactions on Automatic Control, 34, 1, 94-97 (1989) · Zbl 0661.93022 |
| [29] | Xie, L., Output feedback \(H∞\) control of systems with parameter uncertainty, International Journal of Control, 63, 1, 741-750 (1996) · Zbl 0841.93014 |
| [30] | Xie, L., & de Souza, C.E. (1995). On robust filtering for linear systems with parameter uncertainty. Proceedings of the 34th IEEE conference on decision and control, New Orleans, LA, USA (pp. 2087-2072).; Xie, L., & de Souza, C.E. (1995). On robust filtering for linear systems with parameter uncertainty. Proceedings of the 34th IEEE conference on decision and control, New Orleans, LA, USA (pp. 2087-2072). |
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