Extended \(H_{\infty}\) control -- \(H_{\infty}\) control with unstable weights (Q1974007)

This paper presents a complete solution to an extended \(H_\infty\) control problem for a generalized plant comprising a physical system cascaded with weights containing poles in the closed right half-plane. The authors obtain necessary and sufficient conditions for the existence of a solution that guarantees closed-loop stability of the physical system and controller as well as achieving the \(H_\infty\) norm constraint on the closed-loop of the transfer function matrix of the generalized plant and controller interconnection. The set of all feasible controllers is characterized. Conditions for solvability are a minimal variation on those appearing in the standard \(H_\infty\) control problem.