Linear Periodic Systems

Abstract

In this chapter, we set the basis for the study of linear periodic systems in discretetime. We start with the impulse response description, thanks to which the notion of the periodic transfer operator is introduced. Then we move to the periodic input–output difference equation representation (PARMA model). This representation plays a major role in data analysis and periodic systems identification. The characterization in the frequency domain is carried out by means of the concept of exponentially modulated periodic signals. Finally, the state–space representation is discussed and related to the input–output descriptions. Historically, in the literature of the field, the state–space description has received more attention. However, herein we initially adopt an input–output viewpoint for reasons of generality, and postpone to later sections the state–space realm.