Stability Analysis of Discrete-Time Cone-Preserving Systems With Time-Varying Delays

This letter investigates stability issues related to linear discrete-time cone-preserving systems with time-varying delays. The study begins by examining the monotonicity of discrete-time systems with cone invariance. Equivalent asymptotic stability conditions for discrete-time cone-preserving systems with time-varying delays are then provided based on the monotonicity of cone-preserving systems and the comparison principle. The results indicate that time delays do not affect asymptotic stability. Furthermore, the
$\alpha $
-exponential stability is analyzed to characterize the decay rate of the system. Finally, a numerical example is presented to illustrate the theoretical findings. These results contribute to the understanding of stability analysis of cone-preserving systems with time-varying delays.