Mixed ℋ2 and ℋ∞ performance objectives. I. Robust performance analysis

This paper introduces an induced-norm formulation of a mixed ℋ₂ and ℋ_∞ performance criterion. It is shown that different mixed ℋ₂ and ℋ_∞ norms arise from different assumptions on the input signals. While most mixed norms can be expressed explicitly using either transfer functions or state-space realizations of the system, there are cases where the explicit formulas are very hard to obtain. In the later cases, examples are given to show the intrinsic nature and difficulty of the problem. Mixed norm robust performance analysis under structured uncertainty is also considered in the paper