All solutions to the ℋ∞ control synthesis problem with unstable weights

We solve the ℋ_∞ synthesis problems with unstable weights that arise in servo system synthesis problems and estimation problems of unstable plants. The problem solved is in the most general form and no unnecessary assumptions are made. The solution is based on the structure of the comprehensively stable systems and the solution to an algebraic problem with respect to two linear matrix equations and one linear matrix inequality. This provides an approach to the synthesis of servo systems and the estimation problem of unstable plants