Linear Polytopic Positive Invariance

• 成果类型: Article
• 署名作者: Rakovic, Sasa V.; Zhang, Sixing
• 署名单位: Beijing Information Science & Technology University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3660173
• 发表日期: 2026
• 关键词: POLYHEDRAL-SETS; systems; computation; state

摘要

This article revisits verification of positive invariance for polytopic sets with respect to linear dynamics. The existing necessary and sufficient conditions are applicable only to fixed candidate polytopic sets. This article derives alternative necessary and sufficient conditions for two main representations of polytopic sets. These novel necessary and sufficient conditions are derived by utilizing the Minkowski function in primal setting and the support function in dual setting. Developed results enable direct positive invariance verification of fixed candidate polytopic sets, as well as enhanced positive invariance verification allowing for a structurally constrained redesign of candidate polytopic sets. The established necessary and sufficient conditions admit algebraic reformulations as feasibility checks of numerically appealing systems of affine inequalities and equalities indicating strongly their high numerical potential.