H2 properties of H∞ central compensators of singularly perturbed systems

In this paper, H_∞ control of linear time-invariant singularly perturbed systems is studied further. In particular, using a sequential procedure approach that decomposes the two-time-scale H_∞ control problem into slow and fast subproblems, the authors give upper bounds on the stabilizing solutions of the slow and fast H_∞ algebraic Riccati equations. These equations arise in standard H_∞ output feedback control problem of singularly perturbed systems. Then, using the obtained bounds, the authors show that in H_∞ output feedback, the so-called slow and fast central compensators satisfy an interesting H₂ norm bounds. These bounds may be used to find a fast central compensator and a slow central compensator that guarantee an equal compromise between H₂ and H_∞ objectives of the individual subproblems. Moreover, the composite H_∞ central compensator, formed as the parallel connection of the fast with the strictly proper part of the slow compensator, guarantees an equal compromise between H₂ and H _∞ objectives for the full-order system