Comments on "Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties"

In the above mentioned paper by Mahmoud-Muthairi (ibid. vol.39 (1994)) a sufficient condition for memoryless stabilization of a class of uncertain linear systems with a variable-state delay and norm-bounded time-varying uncertainties is derived in terms of an algebraic Riccati equation. This Riccati equation depends on several free matrix variables, and a subsequent result in the paper, Theorem 2, states that failure or success of the stabilization algorithm is independent of the selection of these matrix variables. In this paper, we give a counterexample to this Theorem 2 as well as providing a fix.