New Gradient Optimization Approach for Robust and Minimum Norm Problems in Vibration Systems With Time Delay

The study discusses the robust and minimum norm partial eigenvalues assignment optimization problems in nonsingular vibration systems with time delay via the velocity and displacement feedback controller. Leveraging the no spillover property of vibration systems with time delay, a systematic synthesis framework for parametric controller gains is presented. By employing the receptance matrix and QR decomposition methods, stabilization controllers are formulated through the construction of nonsingular transformation matrices. The developed approach substantially reduces the prerequisite knowledge of vibration systems and eliminates the constraints requiring systems matrices to preserve symmetry. A new gradient‐based optimization method is proposed to discuss the robust and minimum norm controller design by establishing a function that measures the sensitivity of closed‐loop eigenvalues of vibration systems. The ratio of robust and minimum norm comprehensive optimization is indirectly selected by changing the weight factors. The effectiveness of the proposed approach is demonstrated through several numerical examples.