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 f unctions. Such weights are used to achieve asymptotically disturbance atten uation and/or asymptotically reference tracking, and they cannot be handled by the standard H-infinity control theory. For this problem, we present a necessary and sufficient condition to exist a solution using Riccati inequa lities. This condition is derived under no unnecessary assumption to enlarg e the applicability to various control problems. Moreover, introducing the assumption that the image of the zero Vectors of G(12) and G(21) are unique , we obtain a LMI condition in order to check the solvability numerically. A numerical example is presented to demonstrate how to calculate a controll er.