B3 algorithm for robust performances analysis in presence of mixed parametric and dynamic perturbations

The performance robustness of control systems in the presence of both parametric perturbations and unmodeled dynamics is investigated. Assuming polynomial parametric perturbations and H_∞ performances, the problem is reduced to checking the positivity of suitable polynomials. A novel algorithm based on the Bernstein polynomial expansion is proposed. A Bernstein branch and bound (B³ ) algorithm has been implemented using the formulas of Bernstein coefficients on subdivisions in the parameter space. The efficiency of the algorithm is demonstrated on some examples taken from the literature on the robustness analysis of nonlinearity perturbed control systems