Some Techniques for Analysis and Design of Robust Controls
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In this thesis we consider issues concerning the robustness of linear time invariant systems. We first attempt to gain a better understanding of some of the problems involved in the robustness assessment of multivariable systems by analyzing them on a loop by loop basis. Then, we assume norm bounded uncertainty on individual plant elements and explore the robustness of such systems via eigenvalue methods. We obtain results that sometimes are simpler than those obtained using the structured singular value approach. Using spectral analysis and some results from the theory of matrix perturbations we then develop robustness bounds. The bounds provide geometrical insight into the problem and also generate expressions in terms of nominal closed loop maps that can be used for analysis and design.<P>Another topic covered in this thesis is stability robustness in the presence of parametric uncertainty. Here, we find a parametrization of all the compensators that robustly stabilize the perturbed plant. The parametrization is obtained in terms of the coprime factors of the plants corresponding to extremal values of the uncertain parameters. Necessary and sufficient conditions for the simultaneous stabilizability of a continuum of plants are obtained. the results are restricted to the single variate case and a complete analysis is carried out for a single uncertain parameter.