An optimal design of H∞ static output feedback controller using LMI for collocated gyroscopic system

A class of symmetric static output feedback controllers are known to robustly stabilize symmetric collocated second-order linear time invariant systems having positive definite or positive semi-definite coefficient matrices. This paper extends the result to the asymmetric systems which include skew-symmetric gyroscopic terms. We first obtain the condition for static output feedback controllers to guarantee the closed-loop robust stability against model errors. Then an optimal H_∞ design method based on linear matrix inequalities is proposed in order to enhance the disturbance attenuation ability. The properties of obtained controllers are discussed theoretically and numerically.