In the context of next generation instrumentation for current telescope and future Extremely Large Telescopes (ELT), the requirements on the correction of the tip-tilt modes are stringent. In a strong turbulence situation and in the presence of structural vibration of the telescope, tip-tilt mirror saturation phenomena can occur, which can degrade the performance or even destabilize the feedback system that is denoted the windup" effects. In this paper we investigate a control strategy which aims to mitigate the undesirable windup" effects. The approach gives possibilities to ensure the performance of a relevant anti-windup" control strategy invoking the small gain theorem and using the H∞ optimization framework. The proposed control method, based on H∞ optimization, guarantees the stability and performance of the tip-tilt loop.