On solving non-standard ℋ−/ℋ2/∞ fault detection problems

We discuss solvability issues of ℋ−/ℋ2/∞ optimal fault detection problems in the most general setting. A solution approach is presented which successively reduces the initial problem to simpler ones. The last computational step generally may involve the solution of a non-standard ℋ−/ℋ2/∞ optimization problem for which we discuss possible solution approaches. Using an appropriate definition of the ℋ−-index, we provide a complete solution of this problem in the case of ℋ2-norm. Furthermore, we discuss the solvability issues in the case of ℋ∞-norm.