A LMI solution in the H2 optimal problem for singularly perturbed systems

This paper proposes a solution to the infinite time near optimal regulator problem for singularly perturbed system through a LMI formulation. It gives an alternate solution to the Riccati equation approach developed by Kokotovic et al. (1986) for the same problem. As in that approach, the original problem is decomposed into two well behaved reduced order problems: the first one formulated on the slow subsystem and the second on the fast subsystem. The solutions of these problems are combined in order to build a composite controller which is optimal when the singular parameter ε tends to zero. The main advantage of the proposed approach based on LMIs is the possibility to include structural constraints allowing to solve some particular control problems. Among the problems involving structural constraints, pole placement in a sector is explored in this paper