Further Input-to-State Stability Subtleties for Discrete-Time Systems

This technical note considers input-to-state stability analysis of discrete-time systems using continuous Lyapunov functions. The main result reveals a relation between existence of a continuous Lyapunov function and inherent input-to-state stability on compact sets with respect to both inner and outer perturbations. If the Lyapunov function is
K
_∞
-continuous, the result applies to unbounded sets as well.