An Extended Modal Identification for Linear Periodically Time-Varying Systems Based on Stability-Preserving State Transformation

This paper proposes an extended modal identification method to extract the time-varying modes and poles of linear periodically time -varying (LPTV) systems. A set of poles defines a stabilitypreserving transformation relat ing the original LPTV state equation to a constant upper triangular state equation and the time-varying modes contain the informat ion regarding the stability of the original LPTV system. The relation between the time-varying modes and poles is presented. The time-varying modes and poles of LPTV systems are shown to be the extension of the linear time-invariant (LTI) case. The proposed identification method is finally illustrated by a numerical example.