Premium
LMI‐based controller synthesis: A unified formulation and solution
Author(s) -
Masubuchi Izumi,
Ohara Atsumi,
Suda Nobuhide
Publication year - 1998
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/(sici)1099-1239(19980715)8:8<669::aid-rnc337>3.0.co;2-w
Subject(s) - class (philosophy) , norm (philosophy) , parametrization (atmospheric modeling) , convex optimization , control theory (sociology) , mathematics , regular polygon , controller (irrigation) , mathematical optimization , linear matrix inequality , optimization problem , computer science , control (management) , artificial intelligence , agronomy , biology , physics , geometry , quantum mechanics , political science , law , radiative transfer
This paper proposes a unified approach to linear controller synthesis that employs various LMI conditions to represent control specifications. We define a comprehensive class of LMIs and consider a general synthesis problem described by any LMI of the class. We show a procedure that reduces the synthesis problem, which is a BMI problem, to solving a certain LMI. The derived LMI condition is equivalent to the original BMI condition and also gives a convex parametrization of all the controllers that solve the synthesis problem. The class contains many of widely‐known LMIs (for H ∞ norm, H 2 norm, etc.), and hence the solution of this paper unifies design methods that have been proposed depending on each LMI. Further, the class also provides LMIs for multi‐objective performance measures, which enable a new formulation of controller design through convex optimization. © 1998 John Wiley & Sons, Ltd.