Computational Aspects of a Criterion for Robust ℓ∞-Stability of Systems with Repeated Perturbations

Abstract — The class of robust stability problems considered involves structured, repeated, linear time-varying, induced ℓ∞-norm bounded perturbations. A well known sufficient condition for these robust problems follows from the scaled small gain theorem and is stated in the form of a scaled ℓ1-norm minimization problem with block diagonal scaling matrices. A procedure reducing the domain in the search for an optimal scaling matrix, while preserving global optimality, is presented here. I