Robust global stabilization of linear systems with input saturation via gain scheduling |
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Authors: | Bin Zhou Zongli Lin Guangren Duan |
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Affiliation: | 1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin 150001, People's Republic of China;2. Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743‐4743, Charlottesville, VA 22904‐4743, U.S.A. |
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Abstract: | The problem of robust global stabilization of linear systems subject to input saturation and input‐additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation‐based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing ?2‐type gain scheduling controller, which requires the online solution of a state‐dependent nonlinear optimization problem and a state‐dependent ?2 algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input‐additive uncertainties, the proposed controller also partially recovers Teel's ?∞‐type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The ?∞‐type scheduling approach achieves robustness not only with non‐input‐additive uncertainties but also requires the closed‐form solution to an ?∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the ?∞‐type scheduling approach in the absence of non‐input‐additive uncertainties. Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | robust global stabilization input saturation parametric Lyapunov equation low gain feedback gain scheduling nonlinear control |
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