Analysis of singular systems using orthogonal functions

In the paper, the authors clear up some confusion in the analysis of singular systems using Walsh functions which have been used in some previous publications. The authors show that the idea of using Walsh functions with singular systems is not fundamentally flawed, but that some care is required. Specifically, there may not always exist a solution for a given choice for the number of basis functions. It is also emphasised that this problem may also occur in the usual state-space case, which has evidently not been realised in the considerable work done in this area.