Mixed ℋ2/ℒ1 control with low order controllers: a linear matrix inequality approach

This paper addresses the problem of designing stabilizing controllers that minimize the ℋ₂ norm of a certain closed-loop transfer function while maintaining the L₁ norm of a different transfer function below a prespecified level. This problem arises in the context of rejecting both stochastic as well as bounded persistent disturbances. Alternatively, in a robust control framework it can be thought as the problem of designing a controller that achieves good nominal ℋ₂ performance, while at the same time, guaranteeing stability against unmodeled dynamics with bounded induced L_∞ norm. The main result of this paper shows that, for the state feedback case, a suboptimal static feedback controller can be synthesized by a two stage process involving a finite-dimensional convex optimization problem and a line-search