A solvability condition of an extended H/sub /spl infin// control problem using Riccati inequalities

In this paper, we consider an H/sub /spl infin// problem using unstable weighting functions. Such weights are used to achieve asymptotic disturbance attenuation and/or asymptotic reference tracking, and they cannot be handled by the standard H/sub /spl infin// 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 j/spl omega/ invariant zeros of G/sub 12/ and G/sub 21/.