This paper introduces a method for designing structured adaptive laws for ‘almost stable’ systems (systems for which a static output feedback gain is known). Structuring the adaptation law allows the designer to specify different evolutions for each component of the controller. Formulated as linear matrix inequalities, the stability conditions are flexible and can fit the applications specifications. The proposed synthesis procedure is applied on 1‐axis linear models of the detection of electromagnetic emissions transmitted from earthquake regions satellite, and the adaptive control law is successfully tested on a complete 3‐axis simulation benchmark. Results show that the use of the σ‐modification allows solving the problem of dynamics change between coarse and fine pointing situations. The adaptive law provides a fully continuous control, which is compared with an existing hybrid control. Results are shown to be satisfactory