Determining continuous-time state equations from discrete-time state equations via the principalqth root method

Fast computational methods are developed for finding the equivalent continuous-time state equations from discrete-time state equations. The computational methods utilize the direct truncation method, the matrix continued fraction method, and the geometric-series method in conjunction with the principal
q
th root of the discrete-time system matrix for quick determination of the approximants of a matrix logarithm function. It is shown that the use of the principal
q
th root of a matrix enables us to enlarge the convergence region of the expansion of a matrix logarithm function and to improve the accuracy of the approximants of the matrix logarithm function.