Inversion of the nodal admittance matrix by the use of state equations
T.B.M. Neill, Daryn Bond · International Journal of Circuit Theory and Applications · 1973
Abstract Previous methods1–4 for inverting the nodal admittance matrix when the elements are rational functions of the Laplace transform variable s used pivotal techniques. Problems of numerical stability made this type of approach suitable only for quite small circuits. A new method based on diagonalizing the A‐matrix of a set of state equations defining the circuit has greatly improved stability. The state equations are derived directly from the nodal equations using a newly developed algorithm. These equations are then used to compute the inverse of the nodal admittance matrix as a matrix of rational functions of s. An example is presented of the application of these methods to a system of 21 degrees of freedom.