Further comments on "Design of piecewise constant gains for optimal control via Walsh functions"

Chen and Hsalo, describing a control problem via Walsh functions, include an algorithm to compute a coefficient matrix which involves inverting
k
matrices of order
n, k
depending on
m
, the number of Walsh functions used. Actually, only two
n \times n
matrices need be inverted for any
m
. The coefficient matrix, the product of a matrix and the Walsh matrix
W
, converts the Walsh expansion into a block pulse function [1] expansion; the transition matrix is simply related to a single precomputed matrix.