[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992
ABSTRACT The performance robustness of control systems in the presence of both parametric perturb... more ABSTRACT 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
ABSTRACT Tridiagonal matrices are considered which are totally nonnegative, i. e., all their mino... more ABSTRACT Tridiagonal matrices are considered which are totally nonnegative, i. e., all their minors are nonnegative. The largest amount is given by which the single entries of such a matrix can be perturbed without losing the property of total nonnegativity.
this paper, Sherbrooke and Patrikalakis(1993) use Bernstein expansion. Sequences of bounding boxe... more this paper, Sherbrooke and Patrikalakis(1993) use Bernstein expansion. Sequences of bounding boxes for the solutionsto the polynomial system are generated by two different approaches: the firstmethod projects control polyhedra onto a set of coordinate planes and the secondexploits linear programming. But no use of the relationship between theBernstein coefficients on neighbouring subboxes, cf. Subsection 2.2 below, ismade and no existence
[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992
ABSTRACT The performance robustness of control systems in the presence of both parametric perturb... more ABSTRACT 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
ABSTRACT Tridiagonal matrices are considered which are totally nonnegative, i. e., all their mino... more ABSTRACT Tridiagonal matrices are considered which are totally nonnegative, i. e., all their minors are nonnegative. The largest amount is given by which the single entries of such a matrix can be perturbed without losing the property of total nonnegativity.
this paper, Sherbrooke and Patrikalakis(1993) use Bernstein expansion. Sequences of bounding boxe... more this paper, Sherbrooke and Patrikalakis(1993) use Bernstein expansion. Sequences of bounding boxes for the solutionsto the polynomial system are generated by two different approaches: the firstmethod projects control polyhedra onto a set of coordinate planes and the secondexploits linear programming. But no use of the relationship between theBernstein coefficients on neighbouring subboxes, cf. Subsection 2.2 below, ismade and no existence
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