H 2 guaranteed cost control problem of singularly perturbed systems with uncertainties

This paper studies the H 2 guaranteed cost control problem for singularly perturbed linear uncertain systems. This is an extension of the work of Garcia et al . (1998) in the sense that the state aud input matrices are allowed to be uncertain and the new method of calculation for the H 2 norm is presented. Thus, the new technique is applicable to more realistic singularly perturbed linear uncertain systems. Moreover, we propose the k -independent controller by solving the reduced-order algebraic Riccati equation only. Therefore, since we need not solve the full-order algebraic Riccati equation or separate the slow aud fast subsystems based on the existing method, it is easy to construct the stabilizing controller. As another significant improvement, some assumptions made previously are not necessary here. A numerical example is given to show the potential of the proposed technique.