Effects of delay on the stability of special high-dimensional discrete-time delay systems

This paper studies the stability of special high-dimensional discrete-time systems with a single delay. It considers delay effects and characterizes the delay set for the stability of the systems. Results obtained in this paper are as follows. First, a sufficient condition for the delay set to be the whole set is established. This condition is given via matrix norms. Secondly, the delay set are presented for fully coupled high-dimensional systems. The above results are novel and will help to solve the well-known delay margin problems for stabilization and consensus control.