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

We transform an 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 ∞ control problem. An algorithm and examples with invariant zeros on the extended imaginary axis are given. same approach, we also solve the singular ℋ 2 control problem.