Analysis of Constrained Linear Systems Subject to Feedback Matrix Perturbation

This paper considers linear systems subject to actuator saturation and feedback matrix perturbation. By restricting the saturation output in a convex hull, sufficient condition is derived for determining whether an ellipsoid is contractively invariant under the feedback matrix perturbation. Furthermore, the condition is transformed into linear matrix inequalities (LMIs) which can be conveniently solved by convex programming. 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. Numerical examples illustrate the effectiveness of the proposed methods.