Abstract
We consider linear discrete-time plants subjected to exogenous disturbances and initial perturbations induced by the unknown initial conditions. A performance index for the accuracy of filtering is introduced which accounts for the effects of exogenous and initial perturbations on the filtering error over finite and infinite time horizons. Linear generalized H ∞-optimal discrete-time filters in the form of observer are designed, which minimize the criterion adopted. Design is performed by using the minimax approach and the apparatus of linear matrix inequalities.
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Doyle, J.C., Glover, K., Khargonekar, P.P., et al., State-space Solutions to Standard H 2 and H ∞ Control Problems, IEEE Trans. Autom. Control, 1989, vol. 34, no. 8, pp. 831–847.
Balandin, D.V. and Kogan, M.M., Minimax Filtering: γ 0-Optimal Observers and Generalized H ∞-Optimal Filters, Autom. Remote Control, 2013, vol. 74, no. 4, pp. 575–587.
Nagpal, K.M. and Khargonekar, P.P., Filtering and Smoothing in an H ∞ Setting, IEEE Trans. Autom. Control, 1991, vol. 36, no. 2, pp. 152–166.
Balandin, D.V. and Kogan, M.M., Generalized H ∞-Optimal Filtering under External and Initial Perturbatuions, Differ. Equat., 2012, vol. 48, no. 11, pp. 1483–1491.
Boyd, S., El Ghaoui, L., Feron, E., et al., Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM, 1994.
Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (LMI-based Control System Design), Moscow: Fizmatlit, 2007.
Balandin, D.V., Kogan, M.M., Krivdina, L.N., et al., Design of Generalized Discrete-Time H ∞-Optimal Control over Finite and Infinite Intervals, Autom. Remote Control, 2014, vol. 75, no. 1, pp. 1–17.
Balandin, D.V. and Kogan, M.M., Generalized H ∞-Optimal Control as a Trade-off between the H ∞-Optimal and γ-Optimal Controls, Autom. Remote Control, 2010, vol. 71, no. 6, pp. 993–1010.
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Original Russian Text © L.N. Krivdina, 2015, published in Avtomatika i Telemekhanika, 2015, No. 9, pp. 115–124.
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Krivdina, L.N. Generalized H ∞-optimal filtering for discrete-time plants over finite and infinite time horizons. Autom Remote Control 76, 1608–1615 (2015). https://doi.org/10.1134/S0005117915090076
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DOI: https://doi.org/10.1134/S0005117915090076