An optimal design of symmetric H∞ static output feedback controller using LMI for collocated second-order linear system

The symmetric control systems have some interesting properties. This paper studies a class of symmetric system consists of a collocated second-order plant and a static output feedback controller. For the system, it is known that the internal stability and the robustness of the closed-loop system are guaranteed based only on the non-parametric structure condition. Our objective is to propose an optimal H_∞ symmetric controller design method under a generalized non-symmetric control specification for disturbance attenuation. For this purpose, we investigate an existence condition of the symmetric controller for the bounded real lemma, and propose a convex optimization method using linear matrix inequalities.