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On the robustness of multivariable linear feedback systems. (English) Zbl 0581.93019

One of the useful indicators of the robustness of a multivariable linear feedback system is the largest singular value of the nominal closed-loop transfer matrix. It is shown that while comparing different, not necessarily diagonal, closed-loop transfer matrices which have the same diagonal elements, the diagonal closed-loop transfer matrix has the greatest robustness. For plants with not ”too” large parameter uncertainty, this result also guarantees the maximization of disturbance rejection, and the minimization of the control signal ”power” at the plant’s input.

MSC:

93B35 Sensitivity (robustness)
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93B50 Synthesis problems
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