Relaxed LMI Conditions for the Design of Robust Static Output Feedback Controllers⁎

In this paper, we propose new sufficient conditions in terms of linear matrix inequalities (LMIs) for the design of robust static output feedback (SOF) controllers for linear time-invariant systems. With this approach, it is possible to deal with the practical problem of not having all state variables available to be directly measured. Additionally, this strategy considers systems subject to the presence of uncertain parameters in its structure. The proposed LMIs were obtained using the Finsler's Lemma. We also present the employment of two relaxation strategies to improve the feasibility region in the controller design. Moreover, this paper presents the results of a practical implementation in an active suspension system susceptible to a fault in the actuator control signal to evaluate the technique's efficiency.