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Quadratic Stabilization of Discrete-Time Bilinear Systems

  • Nonlinear Systems
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Abstract

We consider the problem of stabilization of discrete-time bilinear control systems. Using the linear matrix inequality technique and quadratic Lyapunov functions, we formulate a method for the construction of the so-called stabilizability ellipsoid having the property that the trajectories of the closed-loop system emanating from the points in the ellipsoid asymptotically tend to the origin. The proposed approach allows for an efficient construction of nonconvex domains of stabilizability of discrete-time bilinear control systems. The results are extended to the robust statement of the problem where the system matrix is subjected to structured uncertainties.

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  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    M. V. Khlebnikov

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Original Russian Text © M.V. Khlebnikov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 7, pp. 59–79.

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Khlebnikov, M.V. Quadratic Stabilization of Discrete-Time Bilinear Systems. Autom Remote Control 79, 1222–1239 (2018). https://doi.org/10.1134/S0005117918070044

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