Normalized coprime factorizations and balancing for unstable nonlinear
systems
J.M.A. Scherpen and A.J. van der
Schaft, Int. J. Contr., 6, Vol. 60 (1994) 1193-1222.
Abstract:
In this paper we first study
the normalized right and left coprime factorizations of a nonlinear system from a state
space point of view. In order to do so,
we introduce the notion of inner and co-inner nonlinear systems.
Secondly we deal with balancing for unstable nonlinear systems. For
linear systems there are several ways to approach this problem, and we generalize the ideas of
balancing the normalized coprime factorization and of LQG balancing to the nonlinear case.
LQG balancing can be seen
as measuring the influence of a state component on a certain future and past energy
function. We extend this interpretation to the nonlinear case. Furthermore we use
the normalized coprime factorization to give another way of balancing the unstable nonlinear
system. We give the relation between these two methods of balancing, which
is similar to the relation in the linear case.
Keywords: balancing, nonlinear systems, normalized coprime factorizations, model reduction.
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