Near Optimal H∞ Tracking for a Compact Set of Plants

Here we consider the problem of providing near optimal performance for a large set of possible models. We adopt the H∞framework in the single-input single-output (SISO) setting with structured uncertainty: a compact set of controllable and observable plant models of a fixed order; we consider the control problem of designing a controller to minimize the worst case performance. We consider two different feedback configurations, and under a mild assumption we prove that a linear periodic controller (LPC) exists which achieves the objective.