This paper considers H∞ control of general linear timeinvariant descriptor systems including irregular or impulsive ones. There have been a number of preceding studies using linear matrix inequalities (LMIs), which deal with descriptor-type controllers of the same size as the systems to be controlled. Necessary and sufficient conditions have been proposed for the existence of such H ∞ controllers, and coefficients of controllers are given by the solutions of LMIs (see, e.g., Masubuchi, Kamitane, Ohara, & Suda, 1997, Rehm & Allgö wer, 2001, Uezato & Ikeda, 1999 and Xu & Lam, 2006). Theoretically, these results are satisfactory