Abstract

In this paper we present a joint model for order reduction for dynamic linear time invariant (LTI) system, which we call SVD-AORA (Singular Value Decomposition-Adaptive Order Rational Arnoldi). The SVD-AORA method is an extension of the SVD-Krylov based method. It is based on linear projection using two projection matrices (V and Z). The 1rst matrix V is generated using the Krylov technique through the AORA method, the second matrix Z is generated using the SVD technique by the resolution of the Lyaponuv equation. After the resolution of the Lyaponuv equation, the solution obtained (The gramian observability matrix go) is decomposed using the SVD technique and thus we obtain the second projection matrix Z. The use of the AORA method enhances the numerical eZciency thanks to its relative lower computation complexity and the use of the SVD technique preserves the stability of the reduced system. The proposed method gives a reduced order model asymptotically stable, captures the essential dynamics of the original model and minimizes the absolute error between the original and the reduced one. The results of the proposed method are compared with other popular approach of order reduction in the literature which is the SVD-Krylov method. The reduced systems obtained by the proposed method have better performance compared to SVD-Krylov method. The method is explained through two numerical systems of different order.