Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems
- 1 November 1991
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 36 (11) , 1228-1240
- https://doi.org/10.1109/9.100932
Abstract
Conditions under which a nonlinear system can be rendered passive via smooth state feedback are derived. It is shown that, as in the case of linear systems, this is possible if and only if the system in question has relative degree one and is weakly minimum phase. It is proven that weakly minimum phase nonlinear systems with relative degree one can be globally asymptotically stabilized by smooth state feedback, provided that suitable controllability-like rank conditions are satisfied. This result incorporates and extends a number of stabilization schemes recently proposed for global asymptotic stabilization of certain classes of nonlinear systems.<>Keywords
This publication has 26 references indexed in Scilit:
- Asymptotic stabilization of minimum phase nonlinear systemsIEEE Transactions on Automatic Control, 1991
- A positive real condition for global stabilization of nonlinear systemsSystems & Control Letters, 1989
- Stability improvement of nonlinear systems by feedbackIEEE Transactions on Automatic Control, 1984
- Connections between finite-gain and asymptotic stabilityIEEE Transactions on Automatic Control, 1980
- New passivity-type criteria for large-scale interconnected systemsIEEE Transactions on Automatic Control, 1979
- L_2-stability of interconnected systems using a reformulation of the passivity theoremIEEE Transactions on Circuits and Systems, 1977
- Stability results for nonlinear feedback systemsAutomatica, 1977
- The stability of nonlinear dissipative systemsIEEE Transactions on Automatic Control, 1976
- Feedback Systems: Input-Output PropertiesJournal of Dynamic Systems, Measurement, and Control, 1975
- On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivityIEEE Transactions on Automatic Control, 1966