This paper presents a simple adaptive multi-periodic repetitive control scheme when the MIMO LTI plant is not necessarily positive real (PR), however it is strictly minimum-phase, the spectrum of high-frequency gain matrix CB is symmetric and lies in the open right/left half complex plane(sign/spectrum definite). The non-identifier-based direct adaptive control technique, which does not need plant parameter information, is used to construct adaptive schemes and the system stability is analysed by Lyapunov second method. The extension to plant under certain non-linear perturbations and an exponential stability scheme are also discussed. Finally, an adaptive proportional plus multi-periodic repetitive control scheme is proposed. The theoretical findings are supported with simulations.

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