A new result on robust stability of discrete-time systems with polytopic uncertainties and time-varying state delay

This paper considers the problem of delay-dependent robust stability criteria for linear discrete-time systems with polytopic parameter uncertainties and time-varying delay. By defining a new Lyapunov-Krasovskii function and incorporating a relaxed parameter-dependent technique combined with the idea of introducing free-weighting matrices to achieve delay dependence, an improved delay-dependent stability criterion is devised in terms of a linear matrix inequality, which are dependent on not only the minimum but also the maximum delay bounds for time-delay systems. It is shown to be less conservative than the robust stability condition proposed in [9] and extend the robust stability criterion of continuous time-delay systems published recently in the literature. A numerical example illustrates the resulting criterion outperforms the existing one.