This paper extends to the discrete-time case some robust stability conditions, recently obtained for continuous-time systems. Those conditions are expressed 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 uncertainty can be more efficiently addressed. Numerical examples are included to illustrate the advantages of the new stability conditions. (C) 1999 Elsevier Science Inc. All rights reserved.296416992738