Multi-objective robust H₂/H_∞ control for structural vibration based on LMI

This paper deals with the robust H₂/H_∞ control problem for structure with dynamic characteristic uncertainties. In the process of designing the controller, uncertain parameters (including mass, stiffness and damping) of structures are introduced into perturbation matrix, meanwhile, both the H_∞ disturbance suppression and the optimal H₂ performances of the closed-loop control system are satisfied simultaneously for all allowable uncertainties. To solve the proposed multi-objective optimization problem, linear matrix inequalities (LMIs) are deduced based on the LMI optimization technology, and LMI toolbox of MATLAB is employed to obtain the output feedback controller. Results of vibration control analysis for a 3-story simplified structure show that the proposed method is efficient and superior.