An iterative-LMI based H2 control of singular perturbation systems

In this paper an iterative LMI based approach for solving the H
₂
control problem using static state feedback for singular perturbation systems is proposed. 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 iterative algorithm, these inequalities are solved through iterative LMI formulation. To show the effectiveness of the proposed algorithm comparing to other standard time-scale decomposition methods, an illustrative example is also provided.