Abstract
In this chapter, we consider the class of uncertain time-delay affine-controlled systems in which a delay is admitted in state variables, and we show that the attractive ellipsoid method allows us to create a feedback that provides the convergence of any state trajectory of the controlled system from a given class to an ellipsoid whose “size” depends on the parameters of the applied feedback. Finally, we present a method for numerical calculation of these parameters that provides the “smallest” zone convergence for controlled trajectories.
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Notes
- 1.
If Z > 0, then using the Schur complement, the inequality xxT ≤ Z can be equivalently rewritten in the standard form \(x^{T}Z^{-1}x \leq 1\).
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Poznyak, A., Polyakov, A., Azhmyakov, V. (2014). Robust Stabilization of Time-Delay Systems. In: Attractive Ellipsoids in Robust Control. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09210-2_9
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DOI: https://doi.org/10.1007/978-3-319-09210-2_9
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