Abstract
Power-series approximations to eigenvalue and eigenvector functions have a role to play in the design of multivariable feedback systems. The convergence and sensitivity properties of these approximations depend on the positions of the branch points of the characteristic function of the appropriate rational transfer function. This paper gives a quantitative treatment of this problem and proposes a set of suitable bounds for the case of isolated as well as “latent” branch points. Given the importance of the locations of the branch points, from a practical viewpoint it is desirable to know whether it is possible to precondition the transfer-function matrix so as to adjust the positions of the branch points. To this end the paper proposes suitable algorithms and concludes with two simple design studies which demonstrate the benefits of preconditioning.
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