This paper begins with a complete description of the complex Poynting theorem, followed by a rigorous study of the generalized resonance in a multi-antenna system. The condition generating the generalized resonance is discussed, which is the balance of the electromagnetic fields energy stored in the antennas open system. The matrix expression of the generalized resonant factor (GRF) is derived. On this basis, the generalized Foster reactance theorem for an arbitrary antenna system is presented and radiation Q is used to further describe the generalized resonance behaviors. Some practical examples have shown that the generalized resonance may take on the phenomena of strong and sharp fields in the near zone and super-directivity in the far zone of the antenna system.
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