Comment on “H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_2$$\end{document} Filtering for Discrete-Time Affine Nonlinear Descriptor Systems”

The objective of Aliyu and Perrier (Circuits Syst Signal Process 31(3):927–943, 2012) is to give a H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_2$$\end{document} filter design method for discrete-time affine nonlinear descriptor systems, where both singular and normal filters were considered. A sufficient condition for the solvability of this problem was given in terms of discrete-time Hamilton–Jacobi–Bellman equations, and in some special cases this condition was reduced to some linear matrix inequalities. However, this linear matrix inequality condition is not correct, which is pointed out in this note.