# Lyapunov Characterizations of Input to Output Stability

@article{Sontag2000LyapunovCO, title={Lyapunov Characterizations of Input to Output Stability}, author={Eduardo Sontag and Yuan Wang}, journal={SIAM J. Control. Optim.}, year={2000}, volume={39}, pages={226-249} }

This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis of the input to state stability property, and the results given here extend their validity to the case when the output, but not necessarily the entire internal state, is being regulated.

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## References

SHOWING 1-10 OF 52 REFERENCES

On characterizations of the input-to-state stability property

- Mathematics
- 1995

We show that the well-known Lyapunov sufficient condition for "input-to-state stability" (ISS) is also necessary, settling positively an open question raised by several authors during the past few…

Input-Output-to-State Stability

- Mathematics, Computer ScienceSIAM J. Control. Optim.
- 2001

This work establishes a complete equivalence between the IOSS property and the existence of a certain type of smooth Lyapunov function, and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.

On the Input-to-State Stability Property

- Mathematics, Computer ScienceEur. J. Control
- 1995

Various equivalent definitions of stability expressed in stability, Lyapunov-theoretic, and dissipation terms are reviewed to sketch some applications to the stabilisation of cascades of systems and of linear systems subject to control saturation.

A notion of input to output stability

- Mathematics1997 European Control Conference (ECC)
- 1997

This paper deals with a notion of "input to output stability” (IOS), which formalizes the idea that outputs depend in an "aymptotically stable" manner on inputs, while internal signals remain…

Sufficient lyapunov-like conditions for stabilization

- Mathematics, Computer ScienceMath. Control. Signals Syst.
- 1989

This paper provides sufficient Lyapunov-like conditions for the possibility of stabilizing a control system at an equilibrium point of its state space and assumes the stabilizing feedback laws are assumed to be smooth except possibly at the equilibrium Point of the system.

Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation

- Mathematics
- 1997

The concepts of stability, attractivity and asymptotic stability for systems subject to restrictions of the input values are introduced and analyzed in terms of Lyapunov functions. A comparison
with…

Output-to-state stability and detectability of nonlinear systems

- Mathematics
- 1997

The notion of input-to-state stability (ISS) has proved to be useful in nonlinear systems analysis. This paper discusses a dual notion, output-to-state stability (OSS). A characterization is provided…

Notions of input to output stability

- Mathematics
- 1999

This paper deals with concepts of output stability. Inspired in part by regulator theory, several variants are considered, which differ from each other in the requirements imposed upon transient…

A Smooth Converse Lyapunov Theorem for Robust Stability

- Mathematics
- 1996

This paper presents a converse Lyapunov function theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems.…

External Stability of Nonlinear Systems

- Mathematics
- 1995

Abstract The aim of this note is to present and characterize a notion of external stability for nonlinear systems. Moreover, relationship with appropriate internal stability properties are discussed.…