Model reduction by moment matching for nonlinear time-delay systems

The model reduction problem by moment matching for nonlinear time-delay systems is studied. The notion of moment developed for linear time-delay systems is extended by means of the center manifold theory. In addition the moments at infinity are characterized for both linear and nonlinear time-delay systems. A parameterized family of models achieving moment matching is given. The parameters can be exploited to derive delay-free reduced order models or time-delay reduced order models with additional properties. The theory is illustrated by the reduction of a neutral differential time-delay equation describing the torsional dynamics of an oilwell drillstring.