Minkowski-Lyapunov Functions: Alternative Characterization and Implicit Representation

TL;DR

This paper introduces a new way to characterize Minkowski-Lyapunov functions that simplifies their computation in any finite dimension and extends naturally to robust invariant set analysis.

Contribution

It provides an alternative characterization of Minkowski-Lyapunov functions that enhances computational efficiency and applies to robust positively invariant sets.

Findings

Derived a new characterization enabling efficient computation.

Applicable to arbitrary finite-dimensional systems.

Facilitates analysis of robust positively invariant sets.

Abstract

An alternative characterization of Minkowski--Lyapunov functions is derived. The derived characterization enables a computationally efficient utilization of Minkowski--Lyapunov functions in arbitrary finite dimensions. Due to intrinsic duality, the developed results apply in a direct manner to the characterization and utilization of robust positively invariant sets.