Robust ℓ₁ performance analysis for linear systems with parametric uncertainties

Abstract

In this contribution, a computational approach for analysing the robust ℓ_∞-gain (or the robust ℓ₁ performance) of uncertain linear systems is developed. In particular, the system's state-space matrices may have a rational dependence on structured parametric time-invariant or time-varying uncertainties. The computation is based on robust semi-definite programming and provides a trade-off between accuracy and computational effort. A novel matrix inequality condition to determine the star-norm of discrete-time systems is derived as an auxiliary result.