New Input-to-State Stability Results by Revisiting Vector Halanay's Inequality

• 成果类型: Article
• 署名作者: Mazenc, Frederic; Malisoff, Michael
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Louisiana State University System; Louisiana State University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3677764
• 发表日期: 2026
• 关键词: systems

摘要

We study vector versions of Halanay's inequality. We provide an input-to-state stability result. Even in the scalar case, we provide tighter bounds than those that were available in the literature. Our key new techniques involve finding componentwise positive vectors in the null spaces of suitable matrices. These matrices are expressible as weighted sums involving the coefficient matrices that occur in the vector versions of Halanay's inequality. We allow time-varying coefficients in our Halanay decay conditions. Other key tools to obtain our tighter bounds include novel applications of the Perron-Frobenius Theorem.