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Bidirectional inductive power transfer (IPT) systems facilitate contactless power transfer between two sides, which are separated by an air gap, through weak magnetic coupling. Typical bidirectional IPT systems are essentially high-order resonant circuits and, therefore, difficult to both design and control without an accurate mathematical model, which is yet to be reported. This paper presents a dynamic model, which provides an accurate insight into the behavior of bidirectional IPT systems. The proposed state-space-based model is developed in a multivariable framework and mapped into frequency domain to compute the transfer function matrix of eight-order bidirectional IPT systems. The interaction between various control variables and degree of controllability of the system are analyzed from the relative gain array and singular values of the system. The validity of the proposed dynamic model is demonstrated by comparing the predicted behavior with that measured from a 1 kW prototype bidirectional IPT system under various operating conditions. Experimental results convincingly indicate that the proposed model accurately predicts the dynamical behavior of bidirectional IPT systems and can, therefore, be used as a valuable tool for transient analysis and optimum controller design.