Resumen de Representation and Stability of Solutions for Impulsive Discrete Delay Systems with Linear Parts Defined by Non-Permutable Matrices

Xianghua Jin, JinRong Wang, Dong Shen

• In this paper, we introduce a modified delayed perturbation of discrete matrix exponential for impulsive linear discrete delay systems with non-permutable matrices. Using the Z-transform method and its alternative method, we derive a clear representation of the solution, which covers both impulsive and non-impulsive cases in the existing literature. Moreover, using the representation of solution, discrete Gronwall’s inequality, and discrete Bihari’s inequality, we establish several results of exponential stability.

  Numerical examples are given to verify these results.