- Title
- Input-to-state stability, integral input-to-state stability, and L₂-gain properties: qualitative equivalences and interconnected systems
- Creator
- Kellett, Christopher M.; Dower, Peter M.
- Relation
- ARC.FT1101000746 & ARC.DP120101549
- Relation
- IEEE Transactions on Automatic Control Vol. 61, Issue 1, p. 3-17
- Publisher Link
- http://dx.doi.org/10.1109/TAC.2015.2418671
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2016
- Description
- Input-to-state stability (ISS) and L₂-gain are wellknown robust stability properties that continue to find wide application in the analysis and control of nonlinear dynamical systems and their interconnections. We investigate the relationship between ISS-type and L₂-gain properties, demonstrating several qualitative equivalences between these two properties via coordinate transformations. In particular, we investigate and clearly specify the relationship between ISS and linear L₂-gain, and between integral ISS and nonlinear L₂-gain. This latter relationship raises an interesting question as it is known that cascade and feedback interconnections of integral ISS systems are not generally well-behaved, whereas we demonstrate that such interconnections for systems with nonlinear L₂-gain are well-behaved. We subsequently present several new sufficient conditions for the stability of interconnected systems derived by exploiting the derived qualitative equivalences.
- Subject
- input-to-state stability (ISS); nonlinear dynamical systems; L₂-gain
- Identifier
- http://hdl.handle.net/1959.13/1321803
- Identifier
- uon:24451
- Identifier
- ISSN:0018-9286
- Language
- eng
- Reviewed
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