INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING Int. J. Adapt. Control Signal Process. (2013) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/acs.2406 Structured adaptive attitude control of a satellite Alexandru-Razvan Luzi 1,2,3, * ,† , Dimitri Peaucelle 2,3 , Jean-Marc Biannic 1 , Christelle Pittet 4 and Jean Mignot 4 1 ONERA, The French Aerospace Lab, 2 avenue Edouard Belin, F-31055 Toulouse, France 2 CNRS, LAAS, 7 avenue du Colonel Roche, F-314000 Toulouse, France 3 Univ. de Toulouse, LAAS, F-314000 Toulouse, France 4 CNES ; DCT/SB/PS ; BPI 1712, 18 avenue E. Belin, F-31401 Toulouse, France SUMMARY 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 pro- cedure 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 simu- lation 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. Copyright © 2013 John Wiley & Sons, Ltd. Received 15 October 2012; Revised 12 March 2013; Accepted 5 April 2013 KEY WORDS: direct adaptive control; satellite attitude control; LMI; passivity 1. INTRODUCTION Adaptive control is a control strategy proposing to make online modification to the control law to improve tracking of reference signals as well as better reject perturbations and uncertainties. One of the adaptive schemes [1–3] is based on the online estimation of the unknown elements (perturbations, uncertainties) and tuning the control law based on their estimation. Another widely used adaptation scheme [4, 5] consists of directly tuning the controller gains, based solely on the measured signals. Often called direct adaptive control, it has the advantage of simplicity with respect to more complex estimation/gain scheduling schemes. For this reason, it is also referred to as simple adaptive control [5]. On the other hand, this scheme has the disadvantage of relying on strong assumptions regarding the system’s properties. Passivity hypothesis are generally made, this is why these adaptive schemes are also called passivity-based adaptive control [6]. The results presented in this paper enter this framework. More precisely, we tackle passivity-based adaptive control in the context of linear systems. It does fit the considered application example and corresponds to a first step before extensions to nonlinear systems. Passivity-based adaptive control was originally restricted to square systems having the same number of inputs and outputs [4]. In addition, the open loop system needed to be hyper-minimum *Correspondence to: Alexandru-Razvan Luzi, ONERA, The French Aerospace Lab, 2 avenue Edouard Belin, F-31055 Toulouse. † E-mail: alexandru.luzi@onera.fr Copyright © 2013 John Wiley & Sons, Ltd.