Fast Eigenvalue Sensitivity Calculations for Special Structures of System Matrix Derivatives

Stability and robust design using a sector nonlinearity approach for nonlinear manufacturing systems

“…According to the dynamic theory, the transient response of a system is decided by its eigenvalues [11,12]. Thus, the robust design of the dynamic system should have eigenvalues that are insensitive to large parameter variations.…”

“…The eigenvalues of the dynamic system play a crucial role in system design. The positions of the eigenvalues critically dictate the system stability, and their sensitivity to parameter variations determine the system robustness [11,12]. Thus, both the positions and variations of the eigenvalues are of vital importance in the design of a dynamic system.…”

Physical parameter sensitivity of system eigenvalues and physical model reduction

“…Such information can be used regularly for structural optimization, and for the improvement of the agreement between analytical and experimental results [8,9]. Furthermore, eigen derivatives can be directly applied to system identification and robust performance tests for structural control systems [8,9]. On the other hand, the eigenvalue sensitivity with respect to a physical parameter gives an estimate of the eigenvalue shift when such parameter is changed.…”

“…For example, knowledge of the eigenvector derivatives with respect to physical parameters can be used to optimize a structural design or minimize its sensitivity to parameters. Such information can be used regularly for structural optimization, and for the improvement of the agreement between analytical and experimental results [8,9]. Furthermore, eigen derivatives can be directly applied to system identification and robust performance tests for structural control systems [8,9].…”

“…Several methods have been proposed to analyze the connection between a system variable and its modes [8][9][10]15,16]. One of these methods, the participation factor approach, has been extensively used for the analysis of power systems [10,11].…”