  The Poisson-Lie (PL) T-duality is a generalized T-duality based on the Lie
algebra of the Drinfel'd double. In particular, when we consider the PL
T-duality of a coset space, the dual space is found to be a generalized coset
space, which is called the dressing coset. In this paper, we investigate an
extension of the dressing cosets to the U-duality setup. We propose the gauged
actions for various branes in M-theory and type IIB theory, where the
generalized metric is constructed by using the Exceptional Drinfel'd Algebra
(EDA) and the gauge algebra is a certain isotropic subalgebra of the EDA. By
eliminating the gauge fields, the gauged action reduces to the standard brane
action on a certain reduced background, which we call the exceptional dressing
coset. We also propose an alternative definition of the exceptional dressing
cosets based on Sfetsos's approach and reproduce a known example of non-Abelian
T-duality in the U-duality-covariant formulation.
