Rigorous stability analysis and error correction of existed results of linear discrete time delay system

Asymptotically stable conditions of linear discrete time delay system and robust stable conditions of the corresponding perturbed system (called this interval system) are setup and proved respectively. Based on the fundamental matrix of the system, equivalent conditions guaranteeing the system asymptotical stability are proposed and the rigorous proof are given. Based on these general conditions, sufficient condition is obtained and some extended results in existed reference are pointed out to be wrong. For the perturbed system, the perturbed range is estimated, in which the perturbed system are robust stability. Some simulated example show that the results obtained in this paper are effective.