Robust H_∞ controller design for generalized mechanical systems: An approach utilizing physical characteristics

We propose an integrated approach of robust controller design for generalized mechanical systems which are composed of interconnected basic mechanical components. More precisely, we assume that the mass is uncertain, and the damping matrix and the stiffness matrix are expressed by a linear combination of several distribution matrices. For this system, we consider a kind of static output feedback with respect to the generalized measurement output vector and its derivative, where the control specification is to require stability of the closed-loop system and certain H_∞ disturbance attenuation level. The structure of the controller is proposed utilizing the mechanical system's physical characteristics. By using the bounded real lemma with the Lyapunov matrix variable focusing on the system matrix's feature, we reduce the control problem to solving simultaneous LMIs with respect to all the variables.