Comments on "Global stability of two linearly interconnected nonlinear systems"

In the above paper, conditions were developed to determine the global stability of two linearly interconnected nonlinear systems. This correspondence points out the redundancy of two of these conditions. It is further shown that the inequalities with respect to the bounds for the nonlinearities should be strict for stability conditions to hold well. In addition, what seems to be a possible source of confusion with regard to the signs of the Popov multipliers for substitution in the conditions is indicated.