Necessary and sufficient conditions for stable H∞ stabilizability

In this paper, the stable H∞ control problem is addressed. It is shown that the stable H∞ control problem is reduced to finding a unimodular matrix such that a two block H∞ optimization problem is solvable. And then it can be solved if an unimodular matrix is selected such that a Nehari problem is solvable. In fact, if the unimodular matrix is selected as a constant matrix, then a previous result is obtained.published_or_final_versio