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 -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. STRUCTURED ADAPTIVE ATTITUDE CONTROL OF A SATELLITE 665 phase, or equivalently 'almost strictly passive' (meaning that there exists a static output feedback u D F 0 y that makes the closed loop asymptotically stable and passive) [5]. These conditions have been relaxed in [7] and in [8,9], for non-square systems for which some linear combination of the outputs (Gy) makes the new weighted system almost strictly passive. An additional extension was proposed in [10] by introducing a parallel feedforward gain (also known as shunt, see [5]). This result shows that a necessary condition for building a passivity-based adaptive control law is the existence of a static output feedback law u D F 0 y, which makes the closed loop system passive with respect to the artificial output Gy C Du. Unfortunately, the choice of F 0 , G, D appeared as a difficult problem. Finally, [11] gave a new method based on convex optimization tools (linear matrix inequality based) for the design of these gains. The method applies to any linear time-invariant (LTI) system that is 'almost stable' (meaning that there exists a static output feedback u D F 0 y that makes the closed loop asymptotically stable). The assumption is thus milder than previous almost strictly passive assumptions. The goal of the paper is to apply and extend these results to solve a satellite attitude control problem.The considered adaptive output feedback law is of the following output feedback type u.t / D K.t/e.t/, where e.t/ D y.t/ y r .t / is the error between the measured output y and the reference signal y r , and where K.t/ is the adaptive gain. Gain and output structuring is proposed,where each gain component K i .t / is adapted independently, according to a differential equation. This differential equation contains a gradient-type term G i ee T i , which drives the gains to stabilizing values, according to passivity properties. The second term of the adaptation equation is a barrier term ˆ.K i F 0i /, keeping the gains inside a bounded variation domain. The last term is the classical -modification i .K i F 0i / [5] that drives the gains asympt...