This paper presents a robust adaptive stabilization scheme for a class of nominally first-order and controllable hybrid time-invariant linear systems involving both continuous and discrete parametrizations and signals. The usual assumptions of inverse stability of the plant and knowledge of the high-frequency gain are not required. The design philosophy relies on the separation of the contributions of continuous and discrete dynamics to the output by generating two associate additive terms to build the control action. The controllability of the nominally estimated plant model is maintained by using a hysteresis switching function. This allows relaxing the assumption of stability of the plant inverse.
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