Controllers which satisfy a closed-loop H∞-norm bound and maximize an entropy integral

The problem of maintaining the H^∞ norm of a standard closed loop below a prespecified tolerance level while maximizing an entropy integral (at a point in the right half plane) is posed and solved by way of the equivalent error system distance problem. All error systems with infinity norm below the tolerance level are parameterized as the linear fractional map of an all-pass matrix and an arbitrary stable contraction. The authors derive the maximum entropy choice for the contraction and a value for the maximum entropy. For the maximum entropy at infinity, it is proved that the arbitrary contraction must be set to zero (the central solution); the maximum entropy in this case is an explicit formula in terms of the realization of the error system. Some motivational remarks are made, and links between entropy, H₂ norms and H₂ optimal control are given