This paper presents a complete solution to the measurement output feedback H∞ control problem subject to asymptotic tracking of an infinite energy reference and the presence of nonproper output weights. Relying on generalized Sylvester-type equations, a set of all stabilizing controllers is characterized, explicitly exhibiting the impacts of the reference signal and the output weight on the resulting con- trollers. Based on this specific parameterization, additional disturbance attenuation is tackled, and both full-order and reduced-order controller synthese are discussed. It is observed that the multiobjective problem is equivalent to a standard problem for an axillary system constructed from the original weighted system with the control input matrix and measurement output matrix being augmented by solutions to gen- eralized Sylvester-type equations. An example is included to show the effectiveness of the present results.