Robustness of Multivariable Feedback Systems: Analysis and Optimal Design

摘要

The robustness of the stability property of multivariable feedback control systems with respect to model uncertainty is studied. By introducing a topological notion of arcwise connectivity, robust stability tests are unified. The 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 is shown that at 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 desirable to minimize the maximum singular value of the complementary sensitivity matrix. A robustness optimization problem is posed as a non-square H sup inf optimization problem. All solutions to the optimization problem are derived, and parameterized by the solutions to an equivalent two-parameter interpolation problem.