2018/05/14 by Marco Mazzola, Mazzola, Marco, Khai T. Nguyen +1
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Reservoir Engineering and Simulation Methods #math.FA
paper · pdf · doi:10.48550/arxiv.1805.05035
13 pages
arxiv created 2018/05/14 · openalex publication_date 2018/05/14 · arxiv updated 2018/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lyapunov's theorem is a classical result in convex analysis, concerning the convexity of the range of nonatomic measures. Given a family of integrable vector functions on a compact set, this theorem allows to prove the equivalence between the range of integral values obtained considering all possible set decompositions and all possible convex combinations of the elements of the family. Lyapunov type results have several applications in optimal control theory: they are used to prove bang-bang properties and existence results without convexity assumptions. Here, we use the dual approach to the Baire category method in order to provide a "quantitative" version of such kind of results applied to a countable family of integrable functions.