Constantly scaled H∞ control problems for pseudo full information problems

Deals with the constantly scaled H_∞ control problem. In general, the solvability condition for this problem is non-convex. However, it is known that the state feedback (SF) and the full information (FI) problems can be reduced to convex problems. We consider a class of problems including the SF and the FI problems as the special cases. The class is characterized by an additional assumption called a pseudo full information (PFI) condition. Assuming the PFI condition, we first derive a solvability condition. This condition involves fewer number of variables than the standard solutions for the constantly scaled H_∞ control problem. Based on this condition, we further give a convex sufficient condition for the solvability. The convex solvability condition for the SF and the FI problems can be regarded as the extreme cases of the derived sufficient condition. Moreover, we show that there exists a simple formula of a possible controller, if the PFI condition is assumed