The Parameter Variation Problem in State Feedback Control Systems

[+] Author and Article Information
W. R. Perkins, J. B. Cruz

Department of Electrical Engineering and Coordinated Science Laboratory, University of Illinois, Urbana, Ill.

J. Basic Eng 87(1), 120-124 (Mar 01, 1965) (5 pages) doi:10.1115/1.3650487 History: Received March 06, 1964; Online November 03, 2011


The plant-parameter variation problem in multivariable linear systems described by state-vector equations is formulated using a new sensitivity measure. This formulation involves a direct comparison of open-loop and state-feedback performance in the presence of parameter variations and provides a basis for guaranteeing the superiority of the feedback design. Results are obtained for both continuous and discrete multi-input, multi-output systems. Furthermore, it is shown for single-input, multi-output plants that a low-sensitivity design is also an optimal feedback-control design with respect to a quadratic performance index. This provides a new interpretation of a similar result previously obtained by Kalman.

Copyright © 1965 by ASME
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