Abstract for: An Eigenvector Approach for Analysing Linear Feedback Systems

Formal analysis plays an important role in understanding how feedback structures drive dynamical behaviour. As we know the state behaviour is determined by a linear combination of behaviour modes (associated with eigenvalues). The weight of each mode is a product of a coefficient and a right eigenvector component. An emerging technique in eigen-based analysis focuses on the behaviour mode weight, together with the behaviour mode (eigenvalue), to identify the dominant feedback structure. The purpose of incorporating the weight analysis is to conduct an overall assessment of how feedback structure influences on the state behaviour. This paper revises the conventional eigensolution to the state trajectory by alternating the behaviour mode coefficient to be a product of the normalized left eigenvector, and the system initial conditions. Therefore, the overall behaviour changes due to the changes in a system element (a link or a pathway) can be fully assessed by calculating the eigenvalue, right and left eigenvector sensitivities. Through studying the eigenvector sensitivity, we observe that the right and left eigenvector sensitivities associated with the same mode cannot be evaluated separately. We present an analytical approach to the eigenvector-related sensitivity computation, i.e., a linear combination of the right and left eigenvector sensitivity.