Authors’ abstract: 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.