Robust Control Problems Under Both Controller And Plant Perturbations

In this dissertation, the robust control problems of linear systems under both controller and plant norm-bounded perturbations are studied. The necessary and sufficient conditions are given for robustness analysis of these problems. And robust stability of a class of disc polynomials is studied in the same framework. In addition, for SISO systems, a new LMI-based controller design method is presented by substituting controller uncertainties Δ(s)(||Δ(s)||∞≤γ) by complex numbers α+βi(α²+β²â‰¤Î³²) and using Bounded Real Lemma. Compared with structured singular value synthesis theory, this method is simpler and more direct. Generally this controller design method has some conservatism, but this conservatism is less than the one caused by transforming |||W₁S| + |W₂T|||∞ < 1 into |||W₁S|² + |w₂T|²||∞ <1/2 in the traditional robust performance problems. And in the case of both controller and plant additive perturbations without weighting functions, this method has not any conservatism. This method can be generalized to MIMO systems, discrete systems, time-delay systems.Finally, A class of negative feedback systems under more than two multiplicative perturbations is studied, it shows that there are some natural relations between quadratic stability and stuctured singular value synthesis theory. Some new contents are established in traditional robust stability and quadratic stability.The main contribution in this dissertation is that a new method is presented for traditional robust control problems based on the substitution Δ(s)(||Δ(s)||∞≤γ) —α+βi(α²+β²â‰¤^γ2) . Many new problems arise with this method, and this method gives some new ideas for robust control problems under more than one perturbations.