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<sup>∞</sup>-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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:355750 |
| Date | January 1985 |
| Creators | Foo, Yung Kuan |
| Contributors | Postlethwaite, Ian |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:b0232383-ed71-42f1-92bc-597cd72c872b |
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