EIGENVALUE-EIGENVECTOR SENSITIVITY ANALYSIS OF LINEAR TIME INVARIANT SINGULAR SYSTEMS

This thesis concentrates on the eigenvalue-eigenvector sensitivity analysis of linear time invariant singular systems. In this thesis the problem of sensitivity analysis of singular systems is considered. To prove eigenvalue-eigenvector sensitivity we used important definitions and concepts like Transfer Function Matrix (TFM), state vec tors, input and output vectors, state matrix, input and output matrix. We have shown that the eigenvalue-eigenvector sensitivity analysis is guaranteed by LTI singu lar systems. So it is important to use application of LTI singular systems theorems to determine eigenvalue-eigenvector sensitivity analysis. In addition to this appropriate formulas for the determination of the changes that the main features of the transfer function undergo due to the disturbances of the system’s parameters are presented. These formulas are useful to analyze as well as to synthesize the stability of dynam ical systems as they give directly all the necessary information about the influence of the parameter changes to the system’s behavior. A number of different numerical examples were given to demonstrate the effectiveness of the thesis result. keywords: linear singular systems, transfer functions, eigenvalues , eigenvectors, robustness.