Automation and Remote Control

, Volume 79, Issue 7, pp 1222–1239 | Cite as

Quadratic Stabilization of Discrete-Time Bilinear Systems

  • M. V. KhlebnikovEmail author
Nonlinear Systems


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.


discrete-time bilinear system quadratic Lyapunov function linear feedback stabilizability ellipsoid domain of stabilizability linear matrix inequalities 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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