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H ∞ control of switched linear discrete‐time systems with polytopic uncertainties
Author(s) -
Zhang Lixian,
Shi Peng,
Boukas ElKebir,
Wang Changhong
Publication year - 2006
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.782
Subject(s) - control theory (sociology) , convex optimization , realization (probability) , linear matrix inequality , discrete time and continuous time , linear system , mathematics , regular polygon , h infinity methods in control theory , set (abstract data type) , noise (video) , linear fractional transformation , mathematical optimization , computer science , robust control , control system , control (management) , engineering , statistics , artificial intelligence , mathematical analysis , geometry , electrical engineering , image (mathematics) , programming language
In this paper, the problem of designing H ∞ state‐feedback controllers for switched linear discrete‐time systems with polytopic uncertainties is investigated. Two approaches on designing robust and parameter‐dependent H ∞ controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem, the desired controllers are obtained, respectively, and different optimal H ∞ noise‐attenuation level bounds of corresponding closed‐loop systems are given as well. The designed controllers have their own advantages and disadvantages regarding the conservatism and realization complexity. An illustrative example emerging in networked control systems (NCS) and numerical simulations are presented to show the applicability and effectiveness of the obtained theoretic results. Copyright © 2006 John Wiley & Sons, Ltd.