Tree-Based Algorithms for the Stability of Discrete-Time Switched Linear Systems Under Arbitrary and Constrained Switching

作     者：Dercole, Fabio Della Rossa, Fabio 

作者机构：Politecn Milan Dipartimento Elettron Informaz & Bioingn I-20133 Milan Italy Univ New Mexico Dept Mech Engn Albuquerque NM 87131 USA 

出 版 物：《IEEE TRANSACTIONS ON AUTOMATIC CONTROL》 (IEEE自动控制汇刊)

年 卷 期：2019年第64卷第9期

页      面：3823-3830页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 

主　　题：Algorithm design and analysis stability analysis - stability criteria switched linear systems systems analysis and design - asymptotic stability uncertain systems 

摘      要：We present a direct approach to study the stability of discrete-time switched linear systems that can be applied to arbitrary switching, as well as when switching is constrained by a switching automaton. We explore the tree of possible matrix products, by pruning the subtrees rooted at contractions and looking for unstable repeatable products. Generically, this simple strategy either terminates with all contracting leafs-showing the system s asymptotic stability-or finds the shortest unstable and repeatable matrix product. Although it behaves in the worst case as the exhaustive search, we show that its performance is greatly enhanced by measuring contractiveness w.r.t. sum-of-squares polynomial norms, optimized to minimize the largest expansion among the system s modes.