A new approach to the sensitivity problem in multivariable feedback system design

A new point of view for the parameter variation problem in linear multivariable systems is proposed. The output deviations due to parameter variations for an open-loop realization are related by a sensitivity matrix to the output deviations due to parameter variations for a closed-loop (feedback) realization. Using a time-domain integral of the square of the error as a performance index, frequency-domain criteria involving the sensitivity matrix are derived. The criteria are sufficient for insuring that the feedback realization is less affected by parameter variations than an open-loop realization having the same nominal transfer characteristic. Furthermore, the criteria are independent of the integration interval involved in the performance index. A numerical example shows how the criteria may be used in designing multivariable control systems.