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A Parameter-Dependent Lyapunov Approach for the Control of Nonstationary LPV Systems

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Abstract

The chapter deals with the control of nonstationary linear parameter varying (NSLPV) systems, and is motivated by interest in the control of nonlinear systems along trajectories, particularly prespecified eventually periodic ones. The synthesis objective is to find a feedback parameter-dependent, time-varying controller, where the controller parameters are the same as those of the plant, such that the closed-loop system is asymptotically stable and the ℓ2-induced norm of the closed-loop input–output mapping is less than some ℓ2-gain performance levelγ. The analysis and synthesis results are given in terms of parameterized linear matrix inequalities (PLMIs), and some of the PLMI relaxation methods available in the literature, such as the sum of squares (SOS) decomposition method and the multiconvexity relaxation technique, are discussed. A fast and easy-to-implement algorithm for online controller construction is also provided.

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Author information

Authors and Affiliations

  1. Aerospace and Ocean Engineering Department, Virginia Tech, Blacksburg, VA, 24061, USA

    Mazen Farhood

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  1. Mazen Farhood
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Correspondence to Mazen Farhood .

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Editors and Affiliations

  1. Dept. Mechanical Engineering, University of Houston, Calhoun Road 4800, Houston, 77204-4006, Texas, USA

    Javad Mohammadpour

  2. , Department of Mathematics, University of Stuttgart, Pfaffenwaldring, Stuttgart, 70569, Germany

    Carsten W. Scherer

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Farhood, M. (2012). A Parameter-Dependent Lyapunov Approach for the Control of Nonstationary LPV Systems. In: Mohammadpour, J., Scherer, C. (eds) Control of Linear Parameter Varying Systems with Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1833-7_5

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  • DOI: https://doi.org/10.1007/978-1-4614-1833-7_5

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  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4614-1832-0

  • Online ISBN: 978-1-4614-1833-7

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