This paper deals with a class of Resistive-Inductive-Capacitive (RLC) circuits and switched RLC (s-RLC) circuits modeled in Brayton Moser framework. For this class of systems, new passivity properties using a Krasovskii's type Lyapunov function as storage function are presented. Consequently, the supply-rate is a 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 convergence to the desired operating point is theoretically proved for both 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.

中文翻译：

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Brayton-Moser 系统控制的微分和无源性

本文涉及一类在 Brayton Moser 框架中建模的电阻-电感-电容 (RLC) 电路和开关 RLC (s-RLC) 电路。对于这类系统，提出了使用 Krasovskii 型李雅普诺夫函数作为存储函数的新被​​动特性。因此，供给率是系统状态、输入及其一阶时间导数的函数。此外，在展示了端口变量的可积性特性之后，提出了两种称为输出整形和输入整形的简单控制方法来调节 RLC 和 s-RLC 电路中的电压。对于所提出的两种控制方法，理论上都证明了到所需操作点的全局渐近收敛。此外，输入整形方法确保了负载不确定性方面的稳健性。