A Feedback Stability Theorem for Frequency-dependent Compensation of Excess and Lack of Passivity
For control engineers, this provides a more flexible stability analysis tool for interconnected systems with non-passive components.
The paper introduces a stability theorem for feedback interconnections of linear time-invariant systems using frequency-dependent passivity indices, enabling stability certification even when both systems lack passivity in scalar terms. A numerical case study demonstrates advantages over scalar indices.
This article studies the stability of feedback interconnections of linear time-invariant systems based on frequency-dependent passivity indices. Using these frequency-dependent passivity indices, we show that the feedback interconnection of two systems can be certified to be stable even if both systems have a lack of passivity in terms of their scalar passivity indices. The main contribution of this paper is a new stability theorem based on frequency-dependent passivity indices. Moreover, we discuss the connection of the proposed feedback stability theorem to prior results based on scalar passivity indices. A numerical case study showcases the advantages of frequency-dependent passivity indices over scalar indices for feedback interconnections of linear systems.