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Inner approximations of domains of attraction for a class of switched systems by computing Lyapunov‐like functions
Author(s) -
Zheng Xiuliang,
She Zhikun,
Liang Quanyi,
Li Meilun
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4010
Subject(s) - lyapunov function , mathematics , intersection (aeronautics) , domain (mathematical analysis) , semidefinite programming , polynomial , attraction , class (philosophy) , computation , boundary (topology) , mathematical optimization , computer science , algorithm , nonlinear system , mathematical analysis , artificial intelligence , linguistics , philosophy , physics , quantum mechanics , engineering , aerospace engineering
Summary Domain of attraction plays an important role in control systems analysis, which is usually estimated by sublevel sets of Lyapunov functions. In this paper, based on the concept of common Lyapunov‐like functions, we propose an iteration method for estimating domains of attraction for a class of switched systems, where the state space is divided into several regions, each region is described by polynomial inequalities, and any region has no intersection among with each other. Starting with an initial inner estimate of domain of attraction, we first present a theoretical framework for obtaining a larger inner estimate by iteratively computing common Lyapunov‐like functions. Then, for obtaining a required initial inner estimate of domain of attraction, we propose a higher‐order truncation and linear semidefinite programming–based method for computing a common Lyapunov function. Successively, the theoretical framework is under‐approximatively realized by using S‐procedure and sum‐of‐squares programming, associated with a coordinatewise iteration idea. Finally, we implement our method and test it on some examples with comparisons. These computation and comparison results show the advantages of our method.