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New robust LMI synthesis conditions for mixed H 2 / H ∞ gain‐scheduled reduced‐order DOF control of discrete‐time LPV systems
Author(s) -
Rosa Tábitha E.,
Morais Cecília F.,
Oliveira Ricardo C.L.F.
Publication year - 2018
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.4365
Subject(s) - control theory (sociology) , discrete time and continuous time , linear matrix inequality , bounded function , mathematics , scalar (mathematics) , computer science , mathematical optimization , lti system theory , norm (philosophy) , linear system , time complexity , control (management) , algorithm , mathematical analysis , statistics , geometry , artificial intelligence , law , political science
Summary This paper investigates the problems of stabilization and mixed H 2 / H ∞ reduced‐order dynamic output‐feedback control of discrete‐time linear systems. The synthesis conditions are formulated in terms of parameterdependent linear matrix inequalities (LMIs) combined with scalar parameters, dealing with state‐space models where the matrices depend polynomially on time‐varying parameters and are affected by norm‐bounded uncertainties. The motivation to handle these models comes from the context of networked control systems, particularly when a continuous‐time plant is controlled by a digitally implemented controller. The main technical contribution is a distinct LMI‐based condition for the dynamic output‐feedback problem, allowing an arbitrary structure (polynomial of arbitrary degree) for the measured output matrix. Additionally, an innovative heuristic is proposed to reduce the conservativeness of the stabilization problem. Numerical examples are provided to illustrate the potentialities of the approach to cope with several classes of discrete‐time linear systems (time‐invariant and time‐varying) and the efficiency of the proposed design conditions when compared with other methods available in the literature.