Abstract
This paper defines a notion of phase for linear time-periodic (LTP) systems by exploiting the numerical ranges of their harmonic transfer functions. Then an LTP small phase theorem for input–output stability of feedback interconnections is formulated and an LTP sectored real lemma is derived for phase computation. We also discuss the time-domain interpretation of phase and the connection between phase and a constrained version of dissipativity. The new concepts and results developed in this paper complement their gain-based counterparts and extend the study of system phase from multi-input multi-output (MIMO) linear time-invariant (LTI) systems to LTP systems.
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