Toward an insensitive H2 control problem solution

In this paper, the insensitive H₂ control problem is rigorously considered in the multi-parametric case. The main contribution of this paper is to show that the insensitive H₂ control problem can be formulated as a standard H₂ control problem with a structural constraint on the controller. It\´s also shown in this paper that the insensitive H₂ control problem can be approximated via an optimization problem with linear objective and so-called BMI constraints. This result gives an idea on the "complexity" of this control design problem. It provides new perspectives for resolution.