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ℋ ∞ filtering for switched discrete‐time systems under asynchronous switching: A dwell‐time dependent Lyapunov functional method
Author(s) -
Xiang Weiming,
Xiao Jian,
Mahmoud Magdi S.
Publication year - 2015
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2513
Subject(s) - dwell time , asynchronous communication , discrete time and continuous time , computer science , control theory (sociology) , filter (signal processing) , lyapunov function , stability (learning theory) , filtering problem , basis (linear algebra) , function (biology) , filter design , mathematics , nonlinear system , telecommunications , artificial intelligence , medicine , clinical psychology , statistics , physics , geometry , control (management) , quantum mechanics , machine learning , evolutionary biology , computer vision , biology
Summary In this article, theℋ ∞filtering problem for switched discrete‐time linear systems under asynchronous switching is addressed in the framework of dwell time, where ‘asynchronous switching’ covers more general and practical cases, for example, the switching lags caused by mode identification process are taken into consideration. Firstly, a novel dwell‐time dependent Lyapunov function (DTDLF) is introduced to solve stability and ℓ 2 gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, so it is convenient to be applied into filter design withℋ ∞performance instead of weightedℋ ∞performance as many other previous results. Thus, on the basis of DTLDF, a dwell‐time dependent filter with time‐varying structure is proposed to achieve the desirable non‐weightedℋ ∞filtering performance. It is notable that the proposed approach can also easily characterize the relationships amongℋ ∞filtering performance, dwell time, and asynchronous time. Two examples are provided to validate the theoretical findings in this paper. Copyright © 2014 John Wiley & Sons, Ltd.