Model Reduction of Weakly Nonlinear Systems

1. INTRODUCTION As the level of detail and intricacy of dynamical system models continues to grow, the essential behaviour of such systems can be lost in a cloud of complexity. Furthermore, numerical simulations of such systems can consume extensive memory resources and take inordinate amounts of time. Consequently, to cope with the growing complexity and dimension-ality of systems, model reduction has become a vital aspect of modern system simulation. Model reduction techniques for linear systems are well studied (e.g. [B. Moore (1981)], [A.C. Antoulas et all. (2001).] and references therein). However, the study of nonlinear systems is much more complicated and the development of model reduction methods for large-scale nonlinear systems represents a formidable challenge. In general, model reduction techniques fall into two categories – moment matching and Krylov techniques and balancing techniques. The present contribution is concerned with the former. The advantage of Krylov-based methods is that matrix-vector multiplications are all that are involved in the formation of the projection matrices that are used to project the system onto a reduced system. Also sparse linear solvers and