A Study on the Convergence of the Interpolation Point Augmentation Method for L₁ and H_∞ Control Problems

Abstract

This paper studies the convergence of the interpolation augmentation method applied to multi-block H_∞ and L₁ control problems. Firstly, it is shown that the norm of the Hankel operator of the augmented 1 block problems converges to the norm of the Hankel Toeplitz operator of the multi block problem for H_∞ problems. Secondly, it is shown that the norm of the upper bound sequence approaches the optimum under some conditions for L₁ 2-block problems to guarantee the suboptimality of the sequence.