Generalized H∞ control theory

The present H^∞ theory has some constraints in application, e.g. it can not deal with the servo problem. This is due to the superfluous requirement for the internal stability of the weighted feedback system In this paper, we alleviate the stability of the feedback system of G and K to admit pure imaginary poles, only assuring the internal stability of the feedback loop of G₂₂ and K. After such generalization of H^∞ control problem, the servo problem is naturally incorporated into the H^∞ synthesis. The solvability condition and the structure of solution are similar to those of the standard H^∞ control problem. The difference lies in the requirement for the solution of Riccati equation. Here instead of stabilizing solution, a solution of Riccati equation called quasi-stabilizing solution is used. Further, we reveal that all invariant zeros of G₁₂ and G₂₁ in the closed left half plane are hidden modes of the generalized H^∞ feedback system for almost all H^∞ controllers.