QUANTITATIVE DESIGN OF ROBUST MULTIVARIABLE CONTROL-SYSTEMS

By a systematic use of the theory of non-negative matrices, and the associated theory of M-matrices, it is possible to derive measures of robustness which overcome the undue conservatism inherent in the use of singular values of measures of robustness for particular types of structured perturbations. Using these ideas, it is shown that for nominal diagonal closed loop transfer matrices, the controller which maximizes robustness is the one that minimizes the Perron root (maximum eigenvalue) of a certain non-negative matrix. From this, a simple criterion for robustness based on the maximum magnification (M//p) of the closed loop transmission functions, and the Perron root of the uncertainty matrix is derived.