Model reduction of nonlinear systems

This paper presents the application in circuit simulation of a method for model reduction of nonlinear systems that has recently been developed for chemical systems. The technique is an extension of the well-known balanced truncation method that has been applied extensively in the reduction of linear systems. The technique involves the formation of controllability and observability gramians either by simulated results or by measurement data. The empirical gramians are subsequently employed to determine a subspace of the full state-space that contains the most significant dynamics of the system. A Galerkin projection is used to project the system onto the subspace to form a lower-dimensional nonlinear model The method is applied to a nonlinear resistor network which is a standard example for exemplifying the effectiveness of a nonlinear reduction strategy.