# A characterization of integral input-to-state stability

@article{Angeli2000ACO, title={A characterization of integral input-to-state stability}, author={David Angeli and Eduardo Sontag and Yuan Wang}, journal={IEEE Trans. Autom. Control.}, year={2000}, volume={45}, pages={1082-1097} }

The notion of input-to-state stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite L/sup 2/ gains. It plays a central role in recursive design, coprime factorizations, controllers for nonminimum phase systems, and many other areas. In this paper, a newer notion, that of integral input-to-state stability (iISS), is studied. The notion of iISS generalizes the…

## 589 Citations

Characterization of integral input-to-state stability for nonlinear time-varying systems of infinite dimension

- MathematicsArXiv
- 2022

. For large classes of inﬁnite-dimensional time-varying control systems, the equivalence between integral input-to-state stability (iISS) and the combination of global uniform asymptotic stability…

A Complete Characterization of Integral Input-to-State Stability and Its Small-Gain Theorem for Stochastic Systems

- MathematicsIEEE Transactions on Automatic Control
- 2020

A Lyapunov-type characterization of integral input-to-state stability (iISS) is developed, which is truly parallel to the deterministic one and allows stochastic noise to be active globally in the state space.

Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions

- MathematicsSIAM Rev.
- 2020

This survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems and motivates the study of ISS property for distributed parameter systems.

Input-to-state stability of infinite-dimensional control systems

- MathematicsMath. Control. Signals Syst.
- 2013

It is shown that for certain classes of admissible inputs, the existence of an ISS-Lyapunov function implies the ISS of a system, and it is proved a linearization principle that allows a construction of a local ISS- Lyap unov function for a system.

Input-to-state stability and integral input-to-state stability of non-autonomous infinite-dimensional systems

- MathematicsInt. J. Syst. Sci.
- 2021

It is proved that for a class of admissible inputs the existence of an ISS Lyapunov function implies the ISS of a system in Banach spaces and it is shown that uniform global asymptotic stability is equivalent to their integral input-to-state stability for non-autonomous generalised bilinear systems overBanach spaces.

CONSTRAINED INPUT-TO-STATE STABILITY OF NONLINEAR SYSTEMS

- Mathematics
- 2005

Abstract Input-to-state stability (ISS), integral-ISS (iISS) and their related notions of input/output stability and detectability have become a useful framework for nonlinear feedback analysis and…

A characterization of integral input-to-state stability for hybrid systems

- MathematicsMath. Control. Signals Syst.
- 2017

A Lyapunov characterization of iISS is given unifying and generalizing the existing theory for pure continuous-time and pure discrete-time systems and providing a maximum allowable sampling period guaranteeing iISS for sampled-data control systems with an emulated controller.

Infinite-Dimensional Input-to-State Stability and Orlicz Spaces

- MathematicsSIAM J. Control. Optim.
- 2018

It is shown that integral input- to-state stability can be characterized in terms of input-to- state stability with respect to Orlicz spaces, and since this work considers linear systems, the results can also be formulated in Terms of admissibility.

A remark on integral input to state stability

- MathematicsProceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)
- 1998

Integral input to state stability (IISS) is a notion which generalizes the concept of finite gain with respect to integral norms, in the same manner that input to state stability (ISS) generalizes…

Small-Gain Conditions for iISS Systems: Some Proofs of Sufficiency and Necessity ∗§

- Mathematics
- 2009

This technical report addresses necessary conditions and sufficient condi- tions for stability of interconnection of nonlinear systems with external inputs. Integral input-to-state stable (iISS)…

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