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State‐feedback disturbance attenuation for polytopic LPV systems with input saturation
Author(s) -
Yun Sung Wook,
Choi Yun Jong,
Park PooGyeon
Publication year - 2009
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.1479
Subject(s) - control theory (sociology) , disturbance (geology) , parameterized complexity , attenuation , lyapunov function , saturation (graph theory) , mathematics , state (computer science) , matrix (chemical analysis) , control (management) , computer science , nonlinear system , physics , algorithm , paleontology , quantum mechanics , artificial intelligence , combinatorics , optics , biology , materials science , composite material
This paper proposes a state‐feedback control law for linear parameter‐varying (LPV) systems with input saturation and disturbances. The proposed control law employs two control parts: a main control part for reducing the restricted ℒ 2 gain from the mismatched disturbance to the controlled output and an extra control part for eliminating the matched disturbance. Owing to this feature, the proposed control law provides a better disturbance attenuation performance than the conventional control law that deals with a unified disturbance regardless of the presence of matched and mismatched disturbances. Further, considering different forms of the feedback gain matrix K (θ( t )) and the Lyapunov function V ( x ( t )), three types of controllers are proposed. For each type, set invariance and the restricted ℒ 2 gain performance conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs) and then converted into linear matrix inequalities (LMIs) by using a parameter relaxation technique. Results from the simulation of numerical examples confirm the effectiveness of the proposed controllers. Copyright © 2009 John Wiley & Sons, Ltd.