Matrix operators for numerically stable representation of stiff linear dynamic systems

A new transformation having features similar to the Laplace transform (but numerically oriented) is developed from the Chebyshev polynomials theory. Signals are represented as vectors of Chebyshev coefficients, and linear subsystems as precomputed matrices. The original problem is preprocessed only once to yield matrix invariants for fast recurrent computations. Theoretical implications of the exact digitizing of a tenth-order transfer function and the reduced-order modeling of a stiff system are discussed