Loading [MathJax]/extensions/MathMenu.js
Characterizations of Input-to-State Stability for Infinite-Dimensional Systems | IEEE Journals & Magazine | IEEE Xplore
Scheduled Maintenance: On Monday, 30 June, IEEE Xplore will undergo scheduled maintenance from 1:00-2:00 PM ET (1800-1900 UTC).
On Tuesday, 1 July, IEEE Xplore will undergo scheduled maintenance from 1:00-5:00 PM ET (1800-2200 UTC).
During these times, there may be intermittent impact on performance. We apologize for any inconvenience.

Characterizations of Input-to-State Stability for Infinite-Dimensional Systems


Abstract:

We prove characterizations of input-to-state stability (ISS) for a large class of infinite-dimensional control systems, including some classes of evolution equations over...Show More

Abstract:

We prove characterizations of input-to-state stability (ISS) for a large class of infinite-dimensional control systems, including some classes of evolution equations over Banach spaces, time-delay systems, ordinary differential equations (ODE), and switched systems. These characterizations generalize well-known criteria of ISS, proved by Sontag and Wang for ODE systems. For the special case of differential equations in Banach spaces, we prove even broader criteria for ISS and apply these results to show that (under some mild restrictions) the existence of a noncoercive ISS Lyapunov functions implies ISS. We introduce the new notion of strong ISS (sISS) that is equivalent to ISS in the ODE case, but is strictly weaker than ISS in the infinite-dimensional setting and prove several criteria for the sISS property. At the same time, we show by means of counterexamples that many characterizations, which are valid in the ODE case, are not true for general infinite-dimensional systems.
Published in: IEEE Transactions on Automatic Control ( Volume: 63, Issue: 6, June 2018)
Page(s): 1692 - 1707
Date of Publication: 25 September 2017

ISSN Information:

Funding Agency:


Contact IEEE to Subscribe

References

References is not available for this document.