Differentiation and Passivity for Control of Brayton-Moser Systems

This article deals with a class of resistive-inductive-capacitive (RLC) circuits and switched RLC (s-RLC) circuits modeled in the Brayton-Moser framework. For this class of systems, new passivity properties using a Krasovskii-type Lyapunov function as storage function are presented, where the supply rate is function of the system states, inputs, and their first time derivatives. Moreover, after showing the integrability property of the port-variables, two simple control methodologies called output shaping and input shaping are proposed for regulating the voltage in RLC and s-RLC circuits. Global asymptotic stability is theoretically proved for both the proposed control methodologies. Moreover, robustness with respect to load uncertainty is ensured by the input shaping methodology. The applicability of the proposed methodologies is illustrated by designing voltage controllers for dc-dc converters and dc networks.