Parlakçı, M. N. Alpaslan2021-02-252021-02-2520141303-62031300-0632https://hdl.handle.net/11411/3313https://doi.org/10.3906/elk-1209-119https://search.trdizin.gov.tr/yayin/detay/213989This paper presents a robust stability problem for linear uncertain discrete-time systems with interval time-varying delay and norm-bounded uncertainties. First, a necessary and sufficient stability condition is obtained by employing a well-known lifting method and switched system approach for nominal discrete-time delay systems. Both the stability method of checking the characteristic values inside the unit circle and a Lyapunov function-based stability result are taken into consideration. Second, a simple Lyapunov-Krasovskii functional (LKF) is selected, and utilizing a generalized Jensen sum inequality, a sufficient stability condition is presented in the form of linear matrix inequalities. Third, a novel LKF is proposed together with the use of a convexity approach in the LKF. Finally, the proposed method is extended to the case when the system under consideration is subject to norm-bounded uncertainties. Three numerical examples are introduced to illustrate the effectiveness of the proposed approach, along with some numerical comparisons.eninfo:eu-repo/semantics/openAccessDiscrete-time systemstime-varying delaynorm-bounded uncertaintiesrobust stabilitylifting methodLyapunov-Krasovskii functionallinear matrix inequalitiesArticle2-s2.0-8489783573610.3906/elk-1209-119213989Q4WOS:000332942900011