This paper considers the problem of asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By using a delay partitioning-based Lyapunov functional, a new criterion for the asymptotic stability of such systems is proposed in terms of linear matrix inequalities (LMIs). The proposed stability condition depends on both the size of delay and partition size. The presented approach is compared with previously reported approaches.
Kokil, P., Kar, H., & Kandanvli, V. K. R. (2011). Stability Analysis of Linear Discrete-Time Systems with Interval Delay: A Delay-Partitioning Approach. ISRN Applied Mathematics, 2011, 1–10. https://doi.org/10.5402/2011/624127