Stability-preserving model order reduction for nonlinear time delay systems

Delay elements are needed to model physical, industrial and engineering systems as action and reaction always come with latency. In this paper, we present an algorithm to obtain the reduced-order models (ROMs) while preserving the stability of nonlinear time delay systems (TDSs), which are approximated first by the piecewise-linear TDSs. One contribution is the derivation of the input-output stability of piecewise-linear TDSs, for the first time. The other is the preservation of the input-output stability of the ROMs. The system matrices are obtained by the left projection matrix from the solution of linear matrix inequalities (LMIs) for the input-output stability test of the original piecewise-linear TDSs and the right projection matrix from matching the estimated moments. An application example then verifies the effectiveness of the proposed method.