  We present a balanced truncation model reduction approach for a class of
nonlinear systems with time-varying and uncertain inputs. First, our approach
brings the nonlinear system into quadratic-bilinear~(QB) form via a process
called lifting, which introduces transformations via auxiliary variables to
achieve the specified model form. Second, we extend a recently developed QB
balanced truncation method to be applicable to such lifted QB systems that
share the common feature of having a system matrix with zero eigenvalues. We
illustrate this framework and the multi-stage lifting transformation on a
tubular reactor model. In the numerical results we show that our proposed
approach can obtain reduced-order models that are more accurate than proper
orthogonal decomposition reduced-order models in situations where the latter
are sensitive to the choice of training data.
