A solvability condition of an extended H-infinity control problem using Riccati inequalities

In this paper, we consider an H-infinity problem using unstable weighting functions. Such weights are used to achieve asymptotically disturbance attenuation and/or asymptotically reference tracking, and they cannot be handled by the standard H-infinity control theory. For this problem, we present necessary and sufficient conditions to exist a solution using Riccati inequalities. This conditions need no assumptions on the jw invariant zeros of G(12) and G(21).