In this note, we provide a proof of necessity for one of the results in [W. M. H. Heemels, J. Daafouz, and G. Millerioux, "Observer-based control of discrete-time LPV systems with uncertain parameters," Automatic Control, IEEE Transactions on, vol. 55, no. 9, pp. 2130-2135, 2010]. This result is essential to the design of discrete-time linear parameter varying (LPV) filters using parameter-dependent poly-quadratic Lyapunov functions. We also provide a brief discussion ofits broader implications on the design of discrete-time LPV filters.