Monotone RLC Circuits

Abstract

Maximal monotonicity is explored as a generalization of the linear theory of passivity, which allows for algorithmic system analysis of an important physical property. The theory is developed for nonlinear 1-port circuits, modelled as port interconnections of the four fundamental elements: resistors, capacitors, inductors and memristors. An algorithm for computing the steady state periodic behavior of such a circuit is presented.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n. 670645.

Oscillations in Mixed-Feedback Systems

“…Here, both A and B are maximal monotone operators. Since, H is a strictly passive operator, H −1 is maximal monotone, by the argument similar to the passivity theorem in [14], [9] and fact that maximal monotonicity is preserved by relational inversion. The main observation from ( 2) is that the mixed-feedback structure translates into the difference of two maximal monotone operators.…”

“…Early connections between maximal monotonicity and passive LTI systems is found in the literature on nonsmooth dynamical systems [20], [21], and fixed point methods are used to compute periodic solutions in nonsmooth Lur'e systems [22]. Recently, In [9], it is shown that the periodic outputs of periodically forced maximal monotone input-output operators, built from port connections of basic circuit elements, can be computed using fixed point methods. The main idea of [9] is as follows.…”

“…Recently, In [9], it is shown that the periodic outputs of periodically forced maximal monotone input-output operators, built from port connections of basic circuit elements, can be computed using fixed point methods. The main idea of [9] is as follows.…”

“…Hence, ( 6) can be solved using fixed point iteration that is known as proximal point method (see [19], Chapter 2). In [9], this approach is used to compute the periodic output of a periodically forced port circuit, where u represents an input current or voltage.…”

“…The negative feedback loop preserves monotonicity, whereas the positive feedback loop locally destroys monotonicity. In recent work, we have explored maximal monotonicity to algorithmically compute the input-output solutions of monotone operators [9]. We follow the same approach here, but extend the algorithm from monotone to mixed-monotone operators.…”