A characterization of integral input-to-state stability
Top Cited Papers
- 1 June 2000
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 45 (6) , 1082-1097
- https://doi.org/10.1109/9.863594
Abstract
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 concept of finite gain when using an integral norm on inputs but supremum norms of states, in that sense generalizing the linear "H/sup 2/" theory. It allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance. We obtain several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations.Keywords
This publication has 23 references indexed in Scilit:
- Notions of input to output stabilitySystems & Control Letters, 1999
- Certainty equivalence implies detectabilitySystems & Control Letters, 1999
- Nonlinear output feedback tracking with almost disturbance decouplingIEEE Transactions on Automatic Control, 1999
- Output-to-state stability and detectability of nonlinear systemsSystems & Control Letters, 1997
- Singular perturbations and input-to-state stabilityIEEE Transactions on Automatic Control, 1996
- L2-Gain and Passivity Techniques in Nonlinear ControlPublished by Springer Nature ,1996
- A Smooth Converse Lyapunov Theorem for Robust StabilitySIAM Journal on Control and Optimization, 1996
- A class of globally stabilizing controllers for nonlinear systemsSystems & Control Letters, 1995
- A state-space approach to parameterization of stabilizing controllers for nonlinear systemsIEEE Transactions on Automatic Control, 1995
- Small-gain theorem for ISS systems and applicationsMathematics of Control, Signals, and Systems, 1994