Eigenvalues, Eigenvectors and Singular Values in Robust Stability Analysis

摘要

Direct incorporation of structured uncertainty in the elements of a multivariable plant into robust stability analyses is described. The use of characteristic locus structure of the nominal plant is demonstrated and it is seen that skewness of the eigenvector matrix has a significant effect on robustness by reducing stability margins. In the worst cases, the techniques are highly sensitive to uncertainty in the vicinity of branch points. The use of unitary transformations removes the problem in the use of eigenvalues and singular values, but at the expense of increased complexity of the result as the transformations interact with the uncertainty to effect stability margins. This is to be expected, however, as eigenvalue and/or singular value information on nominal plant dynamics is not defined in the natural input-output basis.