Weights determine stability of sensitivity-optimal controllers
The author discusses the problem of how to choose the dynamic weight in \(H^\infty\) optimality design to ensure stability and minimum-phase property of the optimal controller. It is shown that for a large class of SISO plants including distributed parameter systems with poles and zeros on the imaginary axis and infinity the necessary and sufficient condition for existence of stable \(H^\infty\) optimal controller for weighted sensitivity is stabilizability of the plant by any stable controller. Necessary and sufficient interpolation conditions on the weight ensuring stability of the optimal controller are formulated and a resulting procedure for controller design is presented. The plant is supposed to have at least one zero in the closed right half-plane. The results for weighted mixed sensitivity minimization for the same class of plants are similar but there are not suggestions how to select mixed sensitivity weights. In the case of lumped parameter plants the results simplify and may be easily implemented. The author presents a number of such examples and explains the mathematical simplifications in these cases. The distributed parameter example analyzed in the paper is a flexible beam with free ends.
scientific article; zbMATH DE number 1062912