Differentially passive circuits that switch and oscillate
For circuit designers, it provides a theoretical framework to analyze nonlinear circuits (switching/oscillating) using passivity, but the results are demonstrated on basic known architectures, making it incremental.
The paper extends passivity theory to analyze switching and oscillating circuits by using differential passivity, enabling quantitative design and analysis of nonlinear circuits like linear ones.
The concept of passivity is central to analyze circuits as interconnections of passive components. We illustrate that when used differentially, the same concept leads to an interconnection theory for electrical circuits that switch and oscillate as interconnections of passive components with operational amplifiers (op-amps). The approach builds on recent results on dominance and p-passivity aimed at generalizing dissipativity theory to the analysis of non-equilibrium nonlinear systems. Our paper shows how those results apply to basic and well-known nonlinear circuit architectures. They illustrate the potential of dissipativity theory to design and analyze switching and oscillating circuits quantitatively, very much like their linear counterparts.