Automation and Remote Control

, Volume 80, Issue 8, pp 1390–1402 | Cite as

Optimization of Bilinear Control Systems Subjected to Exogenous Disturbances. II. Design

  • M. V. KhlebnikovEmail author
Nonlinear Systems


We obtain and discuss new results related to control design for bilinear systems subjected to arbitrary bounded exogenous disturbances. A procedure for the construction of the stabilizability ellipsoid and the domain of stabilizability for bilinear control systems is proposed and its efficiency is proved. This problem is solved both in continuous and discrete time. The main tool is the linear matrix inequality technique. This simple yet general approach is of great potential and can be widely generalized; for instance, to various robust statements of the problem.


bilinear control systems exogenous bounded disturbances quadratic Lyapunov functions linear feedback stabilizability ellipsoid domain of stabilizability linear matrix inequalities 


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This work was partially supported by the Russian Foundation for Basic Research, project no. 18-08-00140. The author would like to thank B.T. Polyak for his interest in this work, fruitful discussions, and useful suggestions.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

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

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