Comment on “Further Enhancement on Robust Control Design for Discrete-Time Singular Systems”

In the above paper, a robust H_∞ 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 the above paper and its consequences do not hold. Then, the robust H_∞ 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.