Robust control Minkowski–Lyapunov functions

Abstract

This article introduces, and studies, the robust control Minkowski–Lyapunov inequality, which is a natural generalization of the recently introduced control Minkowski–Lyapunov inequality. The generalization considers the setting of parametrically uncertain linear discrete time systems. The necessary and sufficient conditions for the characterization and existence of Minkowski functions that verify the robust control Minkowski–Lyapunov inequality are derived. The article also characterizes, and establishes topological properties of, the corresponding robustly stabilizing set-valued control map.