Robustness bound estimates, based on the direct Lyapunov method for discrete-time nominally linear systems, are analysed and compared. Although various robustness bound estimates were introduced recently, little effort has been made to compare them. We develop a scheme for obtaining the estimates, which brings a new robustness bound estimate and provides a useful tool for the study and comparison of a variety of the estimates. A novel technique is presented to compare two superior robustness estimates. The results obtained are illustrated on several examples,