Robust disturbance attenuation with stability for a class of uncertain singularly perturbed systems

In this paper, the problem of robust stability and robust disturbance attenuation is investigated for a class of singularly perturbed linear systems with norm-bounded parameter uncertainties in both state and output equations. Based on the slow and fast subsystems, a composite linear controller is designed such that both robust stability and a prescribed H_∞ infinity performance for the full-order system are achieved, irrespective of the uncertainties. Our results show that the above problem can be converted to an H_∞ infinity control problem for a related singularly perturbed linear system without parameter uncertainty. Thus, the existing results on H_∞ infinity control of singularly perturbed systems can be applied to obtain solutions to the problem of robust H_∞ infinity control for the uncertain systems, which is independent of the singular perturbation epsilon when epsilon is sufficiently small. An example is given to show the potential of the proposed technique.