H2 static state feedback control of linear singular perturbation systems: A new approach

In this paper a new approach for solving the H
₂
control problem using static state-feedback for LTI singular perturbation systems is proposed which achieves a minimum bound on the H
₂
performance level of closed-loop system. The proposed controller is given in terms of the solution of a set of matrix inequalities independent of singular parameter ε. These inequalities are not in the form of linear matrix inequalities (LMI). By introducing a new algorithm, these inequalities are solved through LMI formulation. To show the effectiveness of the proposed algorithm comparing to other standard time-scale decomposition methods, an illustrative example is also provided.