This paper deals with the problem of quadratic stability analysis and quadr
atic stabilization for uncertain linear discrete-time systems with state de
lay. The system under consideration involves state time delay and time-vary
ing norm-bounded parameter uncertainties appearing in all the matrices of t
he state-space model. Necessary and sufficient conditions for quadratic sta
bility and quadratic stabilization are presented in terms of certain matrix
inequalities, respectively. A robustly stabilizing state feedback controll
er can be constructed by using the corresponding feasible solution of the m
atrix inequalities. Two examples are presented to demonstrate the effective
ness of the proposed approach. (C) 2001 Elsevier Science B.V. All rights re
served.