A class of linear, uncertain discrete-time systems with state delay is considered. We develop an linear
matrix inequality (LMI)-based analysis and redesign procedures for improved robust stability of discretetime
systems with state delay and bounded nonlinearities. Then, we address the robust stabilization using
nominal and resilient feedback designs. In both cases, the trade-off between the size of the controller
gains and the bounding factors is illuminated and incorporated into the design formalism. Seeking computational
convenience, all the developed results are cast in the format of LMIs and several numerical
examples are presented throughout the paper.