This paper is concerned with the problem of dissipative performance control under output regulation constraints for continuous-time descriptor systems. In this problem, an output is to be regulated asymptotically with presence of an infinite-energy exo-system, while a specific dissipative performance from a finite external disturbance to a tracking error has also to be satisfied. Based on a generalized Sylvester equation, the asymptotical regulation objective is achieved and a specific structure of the resulting controller is deduced. Using this structure, the solution to the defined multi-objective control problem is characterized in terms of a set of linear matrix inequalities (LMIs).