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Journal of Control Science and Engineering
Volume 2015, Article ID 383297, 9 pages
Research Article

Loop Shaping Control of Input Saturated Systems with Norm-Bounded Parametric Uncertainty

Instituto Tecnológico de Aeronáutica, Praça Marechal Eduardo Gomes, 50-DCTA, 12228-900 São José dos Campos, SP, Brazil

Received 1 May 2015; Accepted 17 June 2015

Academic Editor: Xiao He

Copyright © 2015 Renan Lima Pereira and Karl Heinz Kienitz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a gain-scheduling control design strategy for a class of linear systems with the presence of both input saturation constraints and norm-bounded parametric uncertainty. LMI conditions are derived in order to obtain a gain-scheduled controller that ensures the robust stability and performance of the closed loop system. The main steps to obtain such a controller are given. Differently from other gain-scheduled approaches in the literature, this one focuses on the problem of loop shaping control design with input saturation nonlinearity and norm-bounded uncertainty to reduce the effect of the disturbance input on the controlled outputs. Here, the design problem has been formulated in the four-block synthesis framework, in which it is possible to describe the parametric uncertainty and the input saturation nonlinearity as perturbations to normalized coprime factors of the shaped plant. As a result, the shaped plant is represented as a linear parameter-varying (LPV) system while the norm-bounded uncertainty and input saturation are incorporated. This procedure yields a linear parameter-varying structure for the controller that ensures the stability of the polytopic LPV shaped plant from the vertex property. Finally, the effectiveness of the method is illustrated through application to a physical system: a VTOL “vertical taking-off landing” helicopter.