Generalized $H^{\infty}$ Control Theory

In this paper we formulate and solve a generalized $H^{\infty}$ control problem. The conventional formulation of $H^{\infty}$ problem has some constraints in application, e.g. it can not deal with the servo problem. This is due to the superfluous requirement of internal stability of the augmented system. In this paper, we alleviate the stability of the augmented system to admit pole-zero cancellation on the imaginary aids outside the feedback loop of G22 and K. After such generalization, the servo problem is naturally incorporated into the $H^{\infty}$ synthesis.is.