Balancing & optimization for order reduction of nonlinear systems

This paper considers the problem of passing from a nonlinear time-invariant high-order system to a low-order approximation. At first, a review of some well-known methods for order reduction of nonlinear systems is presented and it is shown that the common feature of many model reduction methods is that they are obtained by applying a projection to system matrices. This resemblance led us to the idea of combining the linear balancing with an optimization procedure for nonlinear systems, resulting in the method of balancing and optimization to be presented here.