Derivation of the maximum entropyH∞-controller and a state-space formula for its entropy

The problem of maximizing the entropy of a stabilized closed-loop system is solved. The solution exploits the parametrization of all closed-loop systems that meet an H ∞-norm bound. The ‘central solution’ of this set is shown to maximize the entropy at infinity and for this case a particularly simple formula is derived for the maximum value of the entropy.