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Polynomial Systems (polynomial + system)

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Engineering100%

Terms modified by Polynomial Systems

  • polynomial system states
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    Selected Abstracts

    Central suboptimal H, filter design for nonlinear polynomial systems

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2009
    Michael Basin
    Abstract This paper presents the central finite-dimensional H, filter for nonlinear polynomial systems, which is suboptimal for a given threshold , with respect to a modified Bolza,Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H, filtering problem to the corresponding optimal H2 filtering problem, using the technique proposed in (IEEE Trans. Automat. Control 1989; 34:831,847). The paper presents the central suboptimal H, filter for the general case of nonlinear polynomial systems based on the optimal H2 filter given in (Int. J. Robust Nonlinear Control 2006; 16:287,298). The central suboptimal H, filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H, filter available for the corresponding linearized system. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2005
    G. Chesi
    Abstract The problem of estimating the domain of attraction (DA) of equilibria is considered for odd polynomial systems. Specifically, the computation of the optimal quadratic Lyapunov function (OQLF), i.e. the quadratic Lyapunov function (QLF) which maximizes the volume of the largest estimate of the DA (LEDA), is addressed. In order to tackle this double non-convex optimization problem, a relaxation approach based on homogeneous polynomial forms is proposed. The first contribution of the paper shows that a lower bound of the LEDA for a fixed QLF can be obtained via linear matrix inequalities (LMIs) based procedures. Also, condition for checking tightness of the lower bound are provided. The second contribution is a strategy for selecting a good starting point for the OQLF search, which is based on the volume maximization of the region where the time derivative of the QLFs is negative and is given in terms of LMIs. Several application examples are presented to illustrate the numerical behaviour of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd. [source]