Premium
ℋ︁ ∞ model reduction for uncertain two‐dimensional discrete systems
Author(s) -
Gao Huijun,
Lam James,
Wang Changhong,
Xu Shengyuan
Publication year - 2005
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.760
Subject(s) - polytope , linearization , mathematics , minification , reduction (mathematics) , norm (philosophy) , state (computer science) , mathematical optimization , linear matrix inequality , linear system , algorithm , mathematical analysis , nonlinear system , discrete mathematics , physics , geometry , quantum mechanics , political science , law
This paper investigates the problem of ℋ ∞ model reduction for two‐dimensional (2‐D) discrete systems with parameter uncertainties residing in a polytope. For a given robustly stable system, our attention is focused on the construction of a reduced‐order model, which also resides in a polytope and approximates the original system well in an ℋ ∞ norm sense. Both Fornasini–Marchesini local state‐space (FMLSS) and Roesser models are considered through parameter‐dependent approaches, with sufficient conditions obtained for the existence of admissible reduced‐order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be readily solved using standard numerical software. In addition, the development of zeroth order models is also presented. Two numerical examples are provided to show the effectiveness of the proposed theories. Copyright © 2005 John Wiley & Sons, Ltd.