H2 guaranteed cost control for singularly perturbed uncertain systems

The H₂ guaranteed cost control problem for a singularly perturbed norm-bounded uncertain system is addressed using the quadratic stabilizability framework. After defining the corresponding slow and fast uncertain subsystems, the set of quadratic stabilizing composite controls is characterized. Two Riccati equations have to be solved, one for the slow subsystem and the other for the fast subsystem. Choosing appropriately the weighting matrices, it is shown how to pick up in the set of quadratic stabilizing composite controls, a control minimizing an upper bound on the H₂ norm of a certain transfer matrix. The case of the guaranteed cost control problem for the reduced system is also investigated