Stability analysis and output-feedback stabilisation of discrete-time systems with an interval time-varying state delay

This study focuses on the stability of discrete-time systems with a time-varying state delay and uncertainties in system matrices. New linear matrix inequality conditions are derived for determining bounds of the delay size to ensure the asymptotic stability. There is no need to assume that the system is stable when the delay vanishes. Conservativeness of the conditions is reduced as much as possible by introducing the free-weighting matrices in a novel way, and using the least inequality in the derivation process. Then a new static output-feedback stabilisation method is proposed with the gain matrix as a direct design variable. Compared with the existing results, the proposed methods indeed give larger delay bounds for many cases.