The passivity of singularly perturbed systems (SPSs) is generally studied without taking advantage of the time-scale separation present in this class of systems. This objective of the presentation is to provide easy-to-verify well-posed conditions characterizing the passivity of a linear SPS starting from the passivity of its associated reduced-order system. To achieve this goal, one can rely on the connection between positive realness and passivity of descriptor systems, as well as the notion of phase for multi-input multi-output (MIMO) systems. A benchmark DC motor is used to illustrate that classical reasoning used for stability analysis of SPSs, which is based on the stability of the reduced-order (slow) and boundary layer (fast) subsystems, cannot be applied to guarantee the passivity of an SPS. On top of that, the presented methodology explains how the time-scale separation can be used to analyze the passivity of general linear time-invariant (LTI) systems.
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