Comment on ``Further Enhancement on Robust H-infinity Control Design for Discrete-Time Singular Systems'

In [1], a robust H1 control design method was presented for uncertain discrete-time singular systems, which was formulated in terms of bilinear matrix inequalities and claimed to be necessary and sufficient. In this note, it is shown that the necessity of Theorem 4 in [1] and its consequences does not hold. Then, the robust H1 control design method in the above paper is only sufficient. It is also noted here that conditions in the rest of the above paper are necessary and sufficient