An Approach to Partial Quadratic Eigenvalue Assignment of Vibration Systems Using Sylvester equations

. This article proposes an approach to resolve the partial eigenvalue assignment output feedback control problem for second-order damped vibration systems. The matrices are prescribed in advance and highly depend on controllability conditions, and the system’s observability eigenvalues are assigned. In addition, the real value spectral decomposition P ( λ ) is exploited to establish conditions so that the feedback gain matrices do not spill over eigenvalue assignment. Thus, the numerical method presented applies to the active vibration control design of multiple inputs and outputs of functional engineering structures. However, it should be noted that the proposed algorithm can present complex computational problems if the mass matrix of the system is almost singular, as it involves the inverse calculation of the mass matrix. Two theorems were presented using Sylvester equations. Three algorithms were implemented based on the Sylvester equation, and examples were presented with their conclusions