Poles and zeros for time-varying systems

Poles and zeros are defined for continuous-time, linear, time-varying systems as functions of time. A pole set defines a stability-preserving variable change relating a time-varying state equation to a diagonal state equation. Zeros are defined using a time-varying transformation of the system's impulse response analogous to the transfer function for time-invariant systems. Both definitions are shown to be generalizations of previous definitions of poles and zeros for time-varying systems by Kamen (1988) and consistent with existing definitions for time-invariant systems. A computation procedure is presented for 2nd order systems and a numerical example is given to illustrate this procedure.