$H_\infty$ control design for an adaptive optics system
Kybernetika, Tome 35 (1999) no. 1, p. [69].

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In this paper we first present a full order $H_\infty $ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order $H_\infty $ controller and demonstrate that the closed-loop (CL) system with the reduced order $H_\infty $ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order $H_\infty $ controller it is found that the dynamical behavior of the reduced order $H_\infty $ controller can be accurately approximated by a single-input, single-output (SISO) transfer function (TF) multiplied by the inverse of the adaptive optics plant dc gain. This observation then leads to a general design methodology which only requires the synthesis of a SISO $H_\infty $ controller and multiplication by constant matrices.
Classification : 93B11, 93B15, 93B36, 93C95
Mots-clés : multi-input; multi-output; adaptive optics system; model reduction techniques; $H_\infty$ control 
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     author = {Denis, Nikolaos and Looze, Douglas and Huang, Jim and Casta\~non, David},
     title = {$H_\infty$ control design for an adaptive optics system},
     journal = {Kybernetika},
     pages = {[69]},
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {1999},
     mrnumber = {1705531},
     zbl = {1274.93060},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/KYB_1999__35_1_a6/}
}
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Denis, Nikolaos; Looze, Douglas; Huang, Jim; Castañon, David. $H_\infty$ control design for an adaptive optics system. Kybernetika, Tome 35 (1999) no. 1, p. [69]. https://geodesic-test.mathdoc.fr/item/KYB_1999__35_1_a6/