In this paper, all operating modes of the ac-dc Ćuk converter have been modeled as linear-time invariant systems where some of the modes were not only modeled but also detected for the first time. Another feature provided in this paper is that the converter can be modeled and analyzed as a switching dynamical system controlled by an external constant duty-ratio switching and the internal switchings shown to be related to the minimum among the time derivatives of a common quadratic Lyapunov function. Some representative simulations are provided to illustrate and validate the technical results of this paper.

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In this paper we design a switching control law for the Ćuk converter in the continuous conduction mode using piecewise linear Lyapunov functions. These Lyapunov functions can be constructed using different number of state variables affecting the system's performance. In the paper, some representative simulations covering construction of different piecewise Lyapunov functions, are provided. @en