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

This paper studies the H-2 guaranteed cost control problem for singularly p erturbed linear uncertain systems. This is an extension of the work of Garc ia 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 pres ented. Thus, the new technique is applicable to more realistic singularly p erturbed linear uncertain systems. Moreover, we propose the epsilon -indepe ndent controller by solving the reduced-order algebraic Riccati equation on ly. Therefore, since we need not solve the full-order algebraic Riccati equ ation or separate the slow aud fast subsystems based on the existing method , it is easy to construct the stabilizing controller. As another significan t improvement, some assumptions made previously are not necessary here. A n umerical example is given to show the potential of the proposed technique.