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This study addresses the control of linear systems subject to both sensor and actuator saturations and additive L2-bounded disturbances. Supposing that only the output of the linear plant is measurable, the synthesis of stabilising output feedback dynamic controllers, allowing to ensure the internal closed-loop stability and the finite L2-gain stabilisation, is considered. In this case, it is shown that the closed-loop system presents a nested saturation term. Therefore, based on the use of some modified sector conditions and appropriate variable changes, synthesis conditions in a dasiaquasidasia- linear matrix inequality (LMI) form are stated in both regional (local) as well as global stability contexts. Different LMI-based optimisation problems for computing a controller in order to maximise the disturbance tolerance, the disturbance rejection or the region of stability of the closed-loop system are proposed.