Reference : Necessary conditions for robust stability of a class of nonlinear systems
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
Necessary conditions for robust stability of a class of nonlinear systems
Goncalves, Jorge mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Dahleh, M. A. mailto [> >]
Pergamon Press - An Imprint of Elsevier Science
Yes (verified by ORBilu)
United Kingdom
[en] Robust stabily ; nonlinear systems ; perturbations ; small gain theorem ; monotone stability
[en] Input-output stability results for feedback systems are developed. Robust stability conditions are presented for nonlinear systems with nonlinear uncertainty defined by some function (with argument equal to the norm of the input) that bounds its output norm. A sufficient small gain theorem for a class of these systems is known. Here, necessary conditions are presented for the vector space (L- infinity ll . ll infinity). These results capture the conservatism of the small gain theorem as it is applied to systems that do not have linear gain. The theory is also developed for the case of L2 signal norms, indicating some difficulties which make this case less natural than L-infinity.

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