Periodic and cut-off responses for linear state-space equations†

Abstract

Two problems are investigated in this paper : (1) The complete response to periodic inputs of a linear time-invariant system or time-varying system with periodically varying parameters is synthesized. When the periodic input is continuous or piecewise continuous, a computational method is established to decompose the complete response of a linear system into two components; the periodic response and the transient response. (2) For inputs which cut off at time t 1, the cut-off response of linear time-invariant or time-varying systems is also analysed. A computational method to obtain the cut-off response for such inputs is derived. Several examples which illustrate the methods are included.