On the Existence and Construction of Common Lyapunov Functions for Switched Discrete Systems

作     者：Kosov, A.A. Kozlov, M.V. 

作者机构：Matrosov Institute for System Dynamics and Control Theory ul. Lermontova 134 Irkutsk664033 Russia National Research Mordovian State University ul. Bol’shevistskaya 68 Saransk430005 Russia 

出 版 物：《Journal of Applied and Industrial Mathematics》 (J. Appl. Ind. Math.)

年 卷 期：2018年第12卷第4期

页      面：668-677页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The authors were supported by the Russian Foundation for Basic Research (project no. 17–31– 50034 mol_nr) 

主　　题：Lyapunov functions 

摘      要：Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a method for its construction is proposed in the form of a combination of the partial Lyapunov functions obtained for isolated subsystems. For a special case of linear three-dimensional systems, some algorithms are proposed for constructing common Lyapunov functions as quadratic and fourth degree forms. Some examples illustrate the effectiveness of the proposed approach. © 2018, Pleiades Publishing, Ltd.