An LMI approach to stability of discrete delay systems

During the last decade, a considerable amount of attention has been payed to stability and control of continuous-time linear systems with delays (see e.g. [?], [?], [?], [?]-[?] and the references therein). Delay-independent and, less conservative, delay-dependent sufficient stability conditions in terms of Riccati or linear matrix inequalities (LMIs) have been derived by using Lyapunov-Krasovskii functionals or Lyapunov-Razumikhin functions. Delay-dependent conditions are based on different model transformations. The most recent one, a descriptor representation of the system [?]-[?], minimizes the overdesign that stems from the model transformation used. The conservatism that stems from the bounding of the cross-terms in the derivation of the derivative of the Lyapunov-Krasovskii functional has also been significantly reduced in the past few years. An important result that improves the standard bounding technique of e.g. [?] has been proposed in [?].