Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations

In this paper we analyze and expand a recently developed approach to Model Order Reduction (MOR) for nonlinear dynamical systems based on trajectory piecewise-linear (TPWL) approximations. Error estimates are given for solutions computed with TPWL reduced order models, and problems of preserving stability and passivity are examined. Since the TPWL method has limited a priori guarantees on global accuracy, its effectiveness is demonstrated on a range of examples including a micromachined switch, two nonlinear electronic circuits, and shock propagation modeled by Burgers’ equation.