Algorithms for optimal control with invariant zeros on the extended imaginary axis

We transform an ℋ∞ℋ∞ control problem with invariant zeros on the extended imaginary axis into a regular problem. Then using the Nevanlinna–Pick theorem, we find necessary and sufficient existence conditions for the original ℋ∞ℋ∞ control problem. An algorithm and examples with invariant zeros on the extended imaginary axis are given.By the same approach, we also solve the singular ℋ2ℋ2 control problem.