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On the stabilization of nonlinear systems

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2 Author(s)
Anantharam, V. ; University of California, Berkeley, CA, USA ; Desoer, C.A.

We extend the applicability of the global Q -parametrization method of controller design to a large class of unstable nonlinear plants. The main result is a two-step compensation theorem analogous to that of Zames for unstable linear plants-if P: L_{e2} \rightarrow L_{e1} is a nonlinear (possibly unstable) plant and F0is any incrementally stable controller such that P_{1}:=P(I - F_{0}(-P))^{-1} is incrementally stable, then the class of controllers F which yields an f.g. stable closed-loop system in the unity feedback configuration for P is globally parametrized by finite gain stable maps Q: L_{e1} \rightarrow L_{e2} with F = F_{0} + Q(I - P_{-1}Q)^{-1}

Published in:

Automatic Control, IEEE Transactions on  (Volume:29 ,  Issue: 6 )