Non-Standard H_∞ Control Problem for Descriptor Systems

Abstract

In this paper a non-standard H_∞ control problem is considered for a generalized plant represented by a descriptor form. This allows that the plant may have invariant zeros at infinity and non-proper. We use properties of a J-lossless matrix and a J-spectral factorization. It is shown that the solvability of the problem is equivalent to the solvability of two generalized Riccati equations. A parametrization is given for all compensators that are not necessarily proper. An existence condition of the proper controllers is considered.