Differentially passive circuits that switch and oscillate

Abstract

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.

Antithetic integral feedback for the robust control of monostable and oscillatory biomolecular circuits

“…We show how the AIF system achieves closedloop regulation and how the same device can be used to design robust oscillatory circuits. The analysis emulates the approach pursued for mechanical and electrical system (Forni and Sepulchre (2014); Miranda-Villatoro et al (2018b)), demonstrating the potential dominance theory has for robustness analysis of AIF circuits.…”

An Optimization Approach to Verifying and Synthesizing K-Cooperative Systems

“…Taking inspiration from the bistable and oscillatory circuits analyzed in Miranda-Villatoro et al (2018, we consider the electrical circuit with three states shown in Fig. 1 (left).…”

Simple use of the Maclaurin series method for linear and non-linear differential equations arising in circuit analysis

“…In sciences and engineering, the analysis of linear and non-linear differential equations is of great importance. Differential equations have appeared in the study of many topics as a robust and quite well-organized mathematical tool, such as circuit problems (Filobello-Nino et al, 2012;Vazquez-Leal et al, 2014Miranda-Villatoro et al, 2018;Popovi c, 2018;Mukhiya et al, 2020), infectious model (Doungmo Goufo et al, 2020;Calatayud et al, 2020aCalatayud et al, , 2020bYüzbas i and _ Ismailov, 2017;Faraz et al, 2020;Khan et al, 2012), soliton wave theory (Khan, 2018(Khan, , 2020a(Khan, , 2020bSaha Ray, 2018), fluid mechanics (Khan, 2013(Khan, , 2014(Khan, , 2011 and many more complex problems (Turkyilmazoglu, 2011;Calatayud et al, 2020aCalatayud et al, , 2020bSlota et al, 2019;He et al, 2019;He, 2019). Suggesting an effective approximate analytical solution to a non-linear differential equation is a challenging task.…”

“…The suggested method is best in its own kind as it gives solutions similar to the numerical method. As the theoretical analysis of the non-linear circuit analysis problems (Filobello-Nino et al, 2012;Vazquez-Leal et al, 2014Miranda-Villatoro et al, 2018;Popovi c, 2018;Mukhiya et al, 2020) has been given considerable attention, which is important for electrical engineering or electronics in the very same way as continuity and momentum equations for fluid mechanics. Circuit design plays a key role in developing successful industrial instruments, such as new electronic devices based on single-electron transistors and memristors.…”