Robust stability/performance of interconnected interval plants with structured norm bounded perturbations

The problem of robust stability and performance for systems with both structured H_∞ and parametric perturbations is considered. The parametric uncertainty is modeled through interconnected interval plants. The structured norm-bounded uncertainty is represented through perturbation blocks representing different uncertainties, such as output sensor errors, neglected high frequency dynamics, input actuator errors, or performance specifications, i.e., input-output sensitivity, and disturbance attenuation. For these types of parametric robust stability/performance problems, it is shown that in order to synthesize a controller that achieves robust performance for the interval plant, it is sufficient to synthesize a controller achieving the goal for much smaller subsets of plants. These sets are obtained by replacing each interval plant by either four real parameters or 32 segments of the interval plant, independently of the plant order. This result allows one to significantly reduce the dimensionality of the μ problem in a μ synthesis approach