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Title: Robustness of multivariable feedback systems : analysis and optimal design
Author: Foo, Yung Kuan
ISNI:       0000 0001 3472 8823
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1985
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The robustness of the stability property of multivariable feedback control systems with respect to model uncertainty is studied and discussed. By introducing a topological notion of arcwise connectivity, existing and new robust stability tests are combined and unified under a common framework. The new switching-type robust stability test is easy to apply, and does not require the nominal and perturbed plants to share the same number of closed right half-plane poles, or zeros, or both. It also highlights the importance of both the sensitivity matrix and the complementary sensitivity matrix in determining the robust stability of a feedback system. More specifically, it is shown that at those frequencies where there is a possibility of an uncertain pole crossing the jw-axis, robust stability is "maximized" by minimizing the maximum singular value of the sensitivity matrix. At frequencies where there is a likelihood of uncertain zeros crossing the imaginary axis, it is then desirable to minimize the maximum singular value of the complementary sensitivity matrix. A robustness optimization problem is posed as a non-square H-optimization problem. All solutions to the optimization problem are derived, and parameterized by the solutions to an "equivalent" two-parameter interpolation problem. Motivated by improvements in disturbance rejection and robust stability, additional optimization objectives are introduced to arrive at the 'best' solution.
Supervisor: Postlethwaite, Ian Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Feedback control systems ; Stability