Iterative design of robust controllers under unknown bounded perturbation norms

A suboptimal robust controller for a multidimensional linear stationary nominal system with output- and control-operator perturbations and a bounded external perturbation is designed. Perturbation norms (weights) are assumed to be unknown and estimated from measurement data. The quality index of the closed-loop control system is taken to be the worst $\ell_\infty$-norm for the output of the system in the class of admissible perturbations. The quality index for systems in the class of linear stationary stabilizing controllers is a fractional linear function of induced norms of transfer matrices of the closed-loop system and perturbation norms. The classical design of suboptimal robust controllers under known perturbation norms is reduced to a standard $\ell_1$-optimization problem, and optimal estimation of unknown perturbation norms is reduced to a linear programming problem. Therefore, the iterative sequential method of controller design and perturbation norm estimation is used as a heuristic method for designing suboptimal robust controllers under unknown perturbation norms. Modeling results corroborate the effectiveness of this method.