Polyhedral Robust Minkowski-Lyapunov Functions

• 成果类型: Article
• 署名作者: Rakovic, Sasa V.; Zhang, Sixing
• 署名单位: Beijing Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3307529
• 发表日期: 2024
• 页码: 3576-3588
• 关键词: Lyapunov methods; Linear matrix inequalities; optimization; Numerical stability; Surveys; Stability criteria; linear programming; Linear inclusions; Minkowski functions; polyhedral sets; robust Lyapunov functions; STABILITY

摘要

This article creates a numerical platform for practical utility of the recently introduced theoretical framework of robust Minkowski-Lyapunov functions. Systems of affine inequalities and equalities whose feasibility verifies the robust Lyapunov nature of polyhedral Minkowski functions with respect to the recently introduced robust Minkowski-Lyapunov inequality are derived. The theoretically exact verification of the robust Minkowski-Lyapunov inequality in the polyhedral setting is reduced to the feasibility stage of a linear program. The topological flexibility of the proposed methods is illustrated by two examples.