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This paper proposes a new method for stability analysis of a bidirectional dual full-bridge dc-dc converter with triple phase-shift control under arbitrary parameter changes. The present analysis makes the stability determination of these power converters more systematic and precise than the existing methods in this field, which are largely based on simulation. Nonlinear and periodic operation of the bidirectional converter is presented including the control circuit. Using the working theory, the converter operation is separated into several stages. Equivalent circuits and state equations are developed for each stage. The Lyapunov function method is used to determine the stability of the converter in every stage. Justification is provided for the absence of abrupt changes of the state variables or infinite noise at the interface of different stages. The stability of the bidirectional converter is determined theoretically by integrating these concepts. Some simulation results are provided to validate the developments.