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Phase wavefront aberrations, which are the effect of atmospheric turbulence, are modelled using the orthogonal set of Zernike polynomials. The first part of this study concerns the derivation of mathematical models for the DM and the atmospheric turbulence. The AO systems used for disturbance rejection concentrate on a specific frequency band, as the disturbance occurs in that region. However, the conventional weighted [Formula: see text] controller is not applicable due to its order. The proposed controller handles this problem by using frequency weighted balanced model reduction. The efficiency of the proposed approach is examined on Zernike\u2019s tip and tilt, focus, astigmatism, coma, trefoil, spherical, secondary astigmatism and quadrafoil modes.<\/jats:p>","DOI":"10.1177\/0142331218780217","type":"journal-article","created":{"date-parts":[[2018,11,27]],"date-time":"2018-11-27T13:10:06Z","timestamp":1543324206000},"page":"2100-2113","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["H\u221e Suboptimal controller design for adaptive optic systems"],"prefix":"10.1177","volume":"41","author":[{"given":"Bilal","family":"Erol","sequence":"first","affiliation":[{"name":"Yildiz Technical University, Control and Automation Engineering Department, Turkey"}]},{"given":"Berk","family":"Alt\u0131ner","sequence":"additional","affiliation":[{"name":"Yildiz Technical University, Control and Automation Engineering Department, 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