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Weighted‐average ℓ 1 filtering for switched positive systems
Author(s) -
Ren Yu,
Sun Guanghui,
Feng Zhiguang,
Er Meng Joo,
Wu Shiqian
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.3850
Subject(s) - control theory (sociology) , filter (signal processing) , bounded function , filter design , dwell time , mathematics , upper and lower bounds , attenuation , stability (learning theory) , linear system , lyapunov function , exponential stability , computer science , nonlinear system , control (management) , medicine , mathematical analysis , clinical psychology , physics , quantum mechanics , artificial intelligence , machine learning , optics , computer vision
Summary In this paper, the filtering problem for a class of switched positive systems with dwell time is investigated. A novel weighted‐average technique is proposed for filter design such that the final estimate of the unmeasurable outputs of the considered system is more accurate than that of traditional approaches. The main contributions of this paper are summarized as follows: By exploiting the positivity and characteristics of switched positive systems with dwell time, a candidate linear copositive Lyapunov function, which is both quasi‐time‐dependent and mode‐dependent, is presented to establish the closed‐loop stability of the considered systems. Upon the established closed‐loop stability, less conservative bounded positive filters (both upper‐bound and lower‐bound filter) with ℓ 1 disturbance attenuation performance are designed for the considered system. By introducing a proper weight, a weighted‐average approach, which is more general than the bounded filter design method, is proposed for filter design. The worst ℓ 1 disturbance attenuation performance of the novel developed filter is evaluated. Both the bounded filters and the weighted‐average filter are designed by solving standard linear programming problems. A numerical example illustrates the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.