Dissipativity analysis of negative resistance circuits

Felix Miranda-Villatoro (1) , Fulvio Forni (2) , Rodolphe Sepulchre (2)

1 TRIPOP - Modélisation, simulation et commande des systèmes dynamiques non lisses
2 CAM - University of Cambridge [UK]

This paper deals with the analysis of nonlinear circuits that interconnect passive elements (capacitors, inductors, and resistors) with nonlinear resistors exhibiting a range of negative resistance. Active elements are necessary to design physical circuits that switch and oscillate. We generalize the classical passivity theory of circuit analysis to develop a port interconnection theory for such non-equilibrium behaviors. The approach closely mimics the classical methodology of (incremental) dissipativity theory, but with dissipation inequalities that combine signed storage functions and signed supply rates to account for the port interconnection of passive and active elements.

Mots clés: Nonlinear circuits; Dissipative systems; Active elements; Limit cycles; Bistability

Domaines: Systèmes dynamiques [math.DS]; Automatique / Robotique; Optimisation et contrôle [math.OC]; Automatique; Systèmes et contrôle [cs.SY]

Felix Miranda-Villatoro, Fulvio Forni, Rodolphe Sepulchre. Dissipativity analysis of negative resistance circuits. Automatica, 2022, 136, pp.110011:1-8. ⟨10.1016/j.automatica.2021.110011⟩. ⟨hal-03472776⟩