Variational Analysis and Generalized Equations in Electronics

Samir Adly (1) , Radek Cibulka (1) , Henri Massias (1)

1 XLIM-DMI - DMI

The paper is devoted to the study of the Aubin/Lipschitz-like property and the isolated calmness of a particular non-monotone generalized equation arising in electronics. The variational and non-smooth analysis is applied in the theory of non-regular electrical circuits involving electronic devices like ideal diodes, practical diodes, DIACs, silicon controlled rectifiers (SCR), and transistors. We also discuss the relationship of our results to the ones using classical techniques from (smooth) analysis and provide a simulation for several simple electrical circuits which are chosen in order to cover the most common non-smooth elements in electronics. The simulations of the electrical circuits discussed in this paper are performed by using Xcos (a component of Scilab).

Mots clés: Non-regular electrical circuits; Aubin/Lipschitz-like property; Isolated calmness; Generalized equation; Non-smooth and variational analysis

Domaines: Mathématiques [math]

Samir Adly, Radek Cibulka, Henri Massias. Variational Analysis and Generalized Equations in Electronics. Set-Valued and Variational Analysis, 2013, 21, pp.333-358. ⟨10.1007/s11228-013-0236-5⟩. ⟨hal-00880703⟩