Input-Output-to-State Stability

TL;DR

This paper establishes a complete Lyapunov-based characterization of input-output-to-state stability (IOSS) for nonlinear systems, generalizing zero-detectability and linking it to norm-estimators and detectability concepts.

Contribution

It provides a full equivalence between IOSS and the existence of a specific smooth Lyapunov function, advancing nonlinear stability theory.

Findings

Proves the equivalence between IOSS and Lyapunov functions.

Shows existence of norm-estimators for IOSS systems.

Characterizes nonlinear detectability via stability and energy estimates.

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.