Model Reduction of Passive Systems through Interpolation of Spectral Zeros. |
|
|
|
|
|
|
| An algorithm is developed for passivity preserving model reduction of linear time invariant systems. Such systems are of great importance in large scale circuit simulation. Implementation schemes are developed for both medium scale (dense) and large scale (sparse) applications. The algorithm is based upon interpolation at selected spectral zeros of the original transfer function to produce a reduced transfer function that has the specified roots as its spectral zeros. These interpolation conditions are satisfied through the computation of a basis for a selected invariant subspace of a certain blocked matrix which has the spectral zeros as its spectrum. Explicit interpolation is avoided and passivity of the reduced model is established, instead, through satisfaction of the necessary conditions of the Positive Real Lemma. It is also shown that this procedure indirectly solves the associated controllability and observability Riccati equations and how to select the interpolation points to give maximal or minimal solutions of these equations. From these, a balancing transformation may be constructed to give a reduced model that is balanced as well as passive and stable. |
|
|
algweb@cerfacs.fr Last Update: Mar 27, 2003 |