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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.
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Lazar et al. (2012) studied this question.
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