We present an algebraic method to compute a globally optimal H2 approximation of order N-3 to a given system of order N. First, the problem is formulated as a two-parameter polynomial eigenvalue problem with a special structure. To solve it, we apply and generalize algebraic techniques used in the computation of the Kronecker canonical form of a matrix pencil. Finiteness of the number of nontrivial solutions then allows the problem to be reduced to a one-parameter polynomial eigenvalue problem, which is solved with standard numerical methods. An example demonstrates the approach and provides a proof of principle.
|Title of host publication||System Identification, the 16th IFAC Symposium on System Identification|
|Publication status||Published - 1 Jan 2012|
|Event||16th IFAC Symposium on System Identification - |
Duration: 11 Jul 2012 → 13 Jul 2012
|Conference||16th IFAC Symposium on System Identification|
|Period||11/07/12 → 13/07/12|
Peeters, R. L. M., Bleylevens, I. W. M., & Hanzon, B. (2012). On Algebraic and Linear Algebraic Aspects of Co-Order Three H2 Model Order Reduction. In System Identification, the 16th IFAC Symposium on System Identification (Vol. 45, pp. 704-709) https://doi.org/10.3182/20120711-3-BE-2027.00379