This paper extends to the discrete-time case some robust stability conditio
ns, recently obtained for continuous-time systems. Those conditions are exp
ressed in terms of Linear Matrix Inequalities (LMI), being thus simply and
efficiently computable. As in the continuous-time case, parameter-dependent
Lyapunov functions can be constructed and, consequently, the new approach
can yield much sharper and less conservative results than the simultaneous
stability approach. In particular, well-known stability problems, namely, D
-stability and robust stability in the presence of diagonally structured un
certainty can be more efficiently addressed. Numerical examples are include
d to illustrate the advantages of the new stability conditions. (C) 1999 El
sevier Science Inc. All rights reserved.