Abstract:

We propose a model reduction method based on the restarted Lanczos process for some large scale linear time-invariant systems. Firstly, we utilize the restarted Lanczos process  to obtain the approximate matrices of both the reachability Gramian matrices and the observability Gramian  matrices of the original system. Then, according to the Lyapunov equations satisfied by the reachability Gramian matrices and the observability Gramian matrices respectively, we can construct the projected Sylvester equations, solve them and carry out the biorthogonal process on the solution to get the required transformation matrices, thus obtaining the order-reduced system of the original system. Using the proposed algorithm to reduce the order of the large scale linear time-invariant system, we can obtain a stable reduced order system in higher precision. Numerical examples verify the effectiveness of the proposed algorithm.

Key words: model order reduction, gramian matrix, restarted Lanczos process, projected Sylvester equation