Transformation of time-variable systems to canonical (phase-variable) form

The problem of transforming a single-input, single-output, time-variable linear system to phase-variable form is considered in this paper. Specific criteria for the existence of an equivalent canonical form are derived together with a method for obtaining the form when it exists. This method, when specialized to fixed systems, is particularly simple, and results in an easilyconstructed explicit form for the transforming matrix. Furthermore, the calculation of eigenvalues and eigenvectors necessary in previously published techniques is avoided.