Approximation of the Constrained Joint Spectral Radius via Algebraic Lifting

• 成果类型: Article
• 署名作者: Xu, Xiangru; Ackmese, Behcet
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Washington; University of Washington Seattle
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3020580
• 发表日期: 2021
• 页码: 3386-3392
• 关键词: Switches; switching systems; Linear systems; Automata; Approximation algorithms; Eigenvalues and eigenfunctions; ELECTRONIC MAIL; Constrained joint spectral radius; constrained switching systems; semitensor product; Switched systems

摘要

This article studies the constrained switching (linear) system which is a discrete-time switched linear system whose switching sequences are constrained by a deterministic finite automaton. The stability of a constrained switching system is characterized by its constrained joint spectral radius that is known to be difficult to compute or approximate. Using the semitensor product of matrices, the matrix-form expression of a constrained switching system is shown to be equivalent to that of a lifted arbitrary switching system. Then, the constrained joint/generalized spectral radius of a constrained switching system is proven to be equal to the joint/generalized spectral radius of its lifted arbitrary switching system which can be approximated by off-the-shelf algorithms.