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On l 1 stability of switched positive singular systems with time‐varying delay
Author(s) -
Li Shuo,
Lin Hai
Publication year - 2016
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.3711
Subject(s) - dwell time , control theory (sociology) , mathematics , stability (learning theory) , convex optimization , exponential stability , class (philosophy) , discrete time and continuous time , regular polygon , mathematical optimization , computer science , nonlinear system , control (management) , statistics , medicine , clinical psychology , physics , geometry , quantum mechanics , artificial intelligence , machine learning
Summary This paper investigates the problem of exponential stability and l 1 ‐gain performance analysis for a class of discrete‐time switched positive singular systems with time‐varying delay. Firstly, a necessary and sufficient condition of positivity for the system is established by using the singular value decomposition method. Then by constructing an appropriate co‐positive Lyapunov functional and using the average dwell time scheme, we develop a sufficient delay‐dependent condition and identify a class of switching signals for the switched positive singular system to be exponentially stable and meet a prescribed l 1 ‐gain performance level under the switching signal. Based on this condition, the decay rate of the system can be tuned and the optimal system performance level can be determined by solving a convex optimization problem. All of the criteria obtained in this paper are presented in terms of linear programming, which suggests a good scalability and applicability to high dimensional systems. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.