Nonlinear L2 gain analysis for linear uncertain saturation systems with feedback perturbation

This paper considers linear uncertain systems subject to input saturation and feedback matrix perturbation. By restricting the saturation output in a convex hull to estimation the domain of attraction, sufficient condition is derived for determining whether an ellipsoid is contractively invariant under the feedback matrix perturbation. In addition, The disturbance rejection ability and L₂ gain analysis method is also considered. Furthermore, All the condition are shown to be transformed into LMIs. Disturbance rejection ability in terms of L₂ gain is also determined by the solution of an LMI optimization problem. Given a reference set, the problem of maximizing the contractively invariant ellipsoid is then proposed and solved using the above mentioned LMIs. Since the feedback matrix is a free parameter in maximizing the contractively invariant ellipsoid, it is used to achieve the minimum estimation sensitivity as an extra optimizing variable. The effectiveness of the proposed methods is illustrated with numerical examples.