Definition of poles of a linear, time-varying system

A definition of poles is presented for continuous-time, linear, time-varying systems. For a linear, time-varying state equation, a set of time-varying poles defines a stability-preserving variable change relating the original state equation to an upper triangular state equation. This definition is shown to be a generalization of existing definitions of poles of a linear, time-varying system and is consistent with the definitions for a linear, time-invariant system. A computation procedure is presented using a QR decomposition of the transition matrix for the state equation. A numerical example is given to illustrate this procedure.