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Asymptotic stability, ℓ 2 gain, boundness analysis, and control synthesis for switched systems: a switching frequency approach
Author(s) -
Xiang Weiming,
Xiao Jian,
Iqbal Muhammad Naveed
Publication year - 2012
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.1287
Subject(s) - control theory (sociology) , stability (learning theory) , switching frequency , basis (linear algebra) , exponential stability , state (computer science) , computer science , control (management) , mathematics , engineering , algorithm , artificial intelligence , physics , nonlinear system , voltage , machine learning , quantum mechanics , electrical engineering , geometry
SUMMARY In this paper, several concepts of switching frequency are introduced to analyze the properties and performance of switched systems in infinite as well as finite‐time intervals. The observation is very motivating that different system properties and performances depend on different switching frequencies. Sufficient conditions ensuring asymptotic stability, ℓ 2 gain performance, and state boundness are derived on the basis of the notions of switching frequency, respectively. Then, on the basis of the analysis results, the control synthesis problems are addressed. LMI‐based design algorithms are proposed to meet different control synthesis requirements. Numerical design examples are provided to demonstrate our results. Copyright © 2011 John Wiley & Sons, Ltd.