Evaluation of matrix polynomials in the state companion matrix of linear time invariant systems
Chris J. Harris · International Journal of Systems Science · 1973
In this paper a new iterative algorithm is presented for the numerical evaluation of matrix polynomials in the state companion matrix of a linear time invariant system. The algorithm also enables the polynomial coefficients of the characteristic equation and the eigenvectors of the state companion matrix to be found. In particular, a truncated series approximation is given for the state transition matrix, providing the most efficient computation known for a prescribed truncation error. The adjustment recursive coefficients used in evaluating the state transition matrix are shown to be on alternative means of evaluating the elements of the inverse Vandermonde matrix of the systems' eigenvalues.