Necessary exponential stability conditions for linear discrete time-delay systems and application

Necessary conditions for the exponential stability of the linear discrete time-delay systems are presented by employing the so-called Lyapunov-Krasovskii functional approach. These conditions not only provide a new tool for stability analysis of the linear discrete time-delay system by characterising instability domains, but also extend the existing results of the linear discrete time-delay system. Simultaneously, we investigate several crucial properties that connect the Lyapunov matrix and the fundamental matrix of the system. Finally, the robust stability analysis of the linear discrete time-delay systems with norm-bounded uncertainties is presented. Numerical examples illustrate the validity of the obtained results.