State-feedback disturbance attenuation for polytopic LPV systems with input saturation

• Published in: International journal of robust and nonlinear control Vol. 20; no. 8; pp. 899 - 922
• Main Authors: Yun, Sung Wook, Choi, Yun Jong, Park, PooGyeon
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 25.05.2010
• Subjects: Attenuation; Control systems; Controllers; disturbance rejection; Disturbances; Gain; gain-scheduled control; input saturation; Law; Linear matrix inequalities; LPV system; parameter-dependent Lyapunov function (PDLF); Saturation; ℒ︁2 gain
• ISSN: 1049-8923; 1099-1239; 1099-1239
• DOI: 10.1002/rnc.1479

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 ℒ︁2 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 ℒ︁2 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.