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Input-Output-to-State Stability

Mikhail Krichman·Eduardo D. Sontag·Yuan Wang
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Abstract

This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of ``norm-estimators'', and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.

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Mikhail Krichman, Eduardo D. Sontag, Yuan Wang. 1999-11-29. Input-Output-to-State Stability. https://arxiv.org/abs/math/9911233

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