Diagonalisation of Second Order Form Model

Second Order Form Model (SOFM) study, needs a reformulation of it transfer function. This can be done by the simultaneous diagonalisation of the SOFM dynamics matrices. The diagonalisation is performed thanks to the Quadratic Eigenvalues Problem. Based on diagonalisation, we show that the inverse Laplace transform of a SOFM can be computed. To preserve the behavior of the model, new input and output matrices are determined to construct diagonal SOFM in the single-input case. An extension to multiple-input is also provided but the solution is based on a model size increasing. Therefore, a partial minimal realisation algorithm for diagonal SOFM is presented. To show the effectiveness of the approach proposed, the method is applied on a numerical example.