Abstract
In this chapter, a particular family of nonlinear affine control systems with a sufficiently general type of uncertainties is considered. Nonlinear uncertain systems, considered here, are governed by vector ordinary differential equations with so-called quasi-Lipschitz right-hand sides admitting a wide class of external and internal uncertainties (including discontinuous nonlinearities such as relay and hysteresis elements, time-delay blocks, and so on). Here, the simplest class of linear state-feedback controllers is analyzed. Sufficient conditions guaranteeing the boundedness of all possible trajectories of controlled systems are presented. Since bounded dynamics can always be imposed on an ellipsoid, it is suggested that the “robust-optimal” gain matrix of the designated linear feedback be selected in such a way that the “size” of this attractive ellipsoid will be minimal. Several numerical and experimental illustrative examples are considered.
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Poznyak, A., Polyakov, A., Azhmyakov, V. (2014). Robust State Feedback Control. In: Attractive Ellipsoids in Robust Control. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09210-2_3
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DOI: https://doi.org/10.1007/978-3-319-09210-2_3
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