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We provide new sufficient conditions for a generalized exponential input-to-state stability condition to hold. Our proofs use innovative trajectory based contractivity and cooperative systems arguments. Another key ingredient is a new variant of Halanay's inequality, which differs from prior Halanay inequalities because of its use of sampling. Our sufficient conditions allow arbitrarily long intervals between some consecutive sampling times, provided the intervals between consecutive sampling times are frequently small enough. This removes a significant limitation of prior results that relied on versions of Halanay's inequality that did not contain sampling. Unlike standard stability conditions, the upper bounds for the norm of the current state in our less restrictive exponential input-to-state stability conclusions have suprema of disturbances over intervals that include earlier times than the initial times. We apply this letter to a broad class of time-varying continuous time systems with sampling.

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IEEE Control Systems Letters

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