Duality bounds in robustness analysis
Using some basic results from convex analysis (Hahn-Banach theorem, Helly theorem), the authors obtaine new bounds for uncertainty, ensuring robust stability of uncertain systems. The line of reasoning goes via a reformulation of the infinite-dimensional multiplier optimization problem resulting from integral quadratic constraints to its dual. The authors consider three cases: the first - with frequency independent constraints leading to frequency dependent multipliers, the second -- with constant multipliers and the third -- with both frequency -- dependent and constant multipliers. This last case leads to the most effective estimates of bounds. Although the optimal solution usually is not available the proper choice of a frequency grid provides a suboptimal solution. This solution seems to be less time consuming than the corresponding suboptimal primal. The authors present simple examples illustrating the results of their theorems dealing with the three types of multipliers mentioned above. Moreover the performance of the suspension of a simple car model is analyzed extensively and numerical results are investigated.
infinite-dimensional multiplier optimization
scientific article; zbMATH DE number 1097586
scientific article