Abstract
In this paper we develop a BMI based method for nonlinear robust stabilization. Robustness against model uncertainty is handled. The development is based on an uncertain multi-model representation of the plant, and an associated piecewise affine state-feedback structure. Assuming a quadratic Liapunov function, a BMI condition for robust (quadratic) stabilization is found. Control constraints are formulated as BMIs or LMIs. A branch-and-bound algorithm is used for solving the BMI problem, that is, finding the unknown quadratic Liapunov function and the piecewise affine state-feedback. Finally, an example is given.
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