Stabilization and L2-gain Analysis of Uncertain Linear Systems with Control Saturation

In this work we consider stabilization and L₂-gain analysis of uncertain linear systems in presence of control saturation and exosystem-disturbances. It is shown that how an invariant and/or attractive domain and the corresponding feedback gain can be found in order to secure a low level L₂-gain with respect to L₂ -disturbances. All of our analysis and design are based on LMIs-constrained optimization, which ensures that (i) the state trajectories starting from the origin have remain inside a bounded ellipsoid, (ii) the ellipsoid is attractive for the disturbance-free systems. At last, the effectiveness of the developed method is illustrated with an example