This article addresses the design problem of linear parameter‐varying (LPV) output feedback controllers that depend on inexact scheduling parameters for LPV systems. This problem has already been tackled and several methods have been proposed by overbounding the discrepancies between the actual scheduling parameters and the provided ones in the derivation of controller design condition. However, all methods in literature have conservatism in the overbounding, which is the main issue addressed in this article. We therefore propose a new overbounding for the discrepancies with the reverse use of Elimination lemma, which introduces no conservatism in theory. The new method is formulated in terms of bilinear matrix inequality, which is not tractable compared with linear matrix inequality, thus a practical design procedure composed of line search and iterative algorithm is shown. The effectiveness of our method is illustrated by an application to flight controller design for the lateral‐directional motions of a research airplane MuPAL‐α and the consequently conducted flight tests.