D-K iteration algorithm for μ-synthesis

For the resulting values of γ and μ in D-K iterations of the μ-synthesis are quite different from each iteration, in solving the optimal problem of the controller K, some eigenvalues of the Hamiltonian matrices, H_∞ and/or J_∞, will be very close to each other during the γ-iteration process, i.e. their eigenvalues will be ill-conditioned, and the γ-iteration will stop at a higher value of γ. In the closed-loop system, the real H_∞-norm obtained by using the resulting K is much lower than that by the γ-iterations. During finding the scaling matrix D(ω), the μ-value obtained by point-wise minimization is also different from that by using the fitted D(ω), and the iterations may not be convergent. The proper steps for D-K iterations are proposed in this paper. A design example is also given by all the intermediate results to illustrate the above mentioned problems of the D-K iteration. The state-space form of the system with parametric uncertainties is also presented for easy use with the D-K iteration commands of the Matlab μ-Tools.