Evaluation of the state transition matrix for linear time invariant systems

Abstract

Abstract In this paper the computation of the transient response of linear time invariant systems is shown to reduce to the computation of an expanded state transition matrix, by adopting the method of auxiliary states to generate system inputs. The evaluation of the composite state transition matrix is shown to be essentially given by the inverse of the transposed confluent Vandermonde matrix of the composite systems' eigenvalues. The inverse of the Vandermonde matrix is given by a now and highly efficient numerical algorithm of the eigenvalue-diagonal transformation type. This algorithm is shown to generate the inversion by a set of recursion equations developed from the composite systems' characteristic equations. These recursion equations are amenable to hand or machine computation and may also be used to evaluate the characteristic equation and its derivatives at sample points other that at its eigenvalues.