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Avtomatika i Telemekhanika, 2018, Issue 7, Pages 59–79 (Mi at14959)  
This article is cited in 6 scientific papers (total in 6 papers)

Nonlinear Systems

Quadratic stabilization of discrete-time bilinear control system

M. V. Khlebnikov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (2268 kB) Citations (6)
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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.
Keywords: discrete-time bilinear system, quadratic Lyapunov function, linear feedback, stabilizability ellipsoid, domain of stabilizability, linear matrix inequalities.
Funding agency Grant number
Russian Science Foundation 16-11-10015
This work was partially supported by the Russian Foundation for Basic Research, project 18-08-00140, and the Russian Science Foundation, project 16-11-10015.
Presented by the member of Editorial Board: L. B. Rapoport

Received: 03.01.2018
English version:
Automation and Remote Control, 2018, Volume 79, Issue 7, Pages 1222–1239
DOI: https://doi.org/10.1134/S0005117918070044
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Khlebnikov, “Quadratic stabilization of discrete-time bilinear control system”, Avtomat. i Telemekh., 2018, no. 7, 59–79; Autom. Remote Control, 79:7 (2018), 1222–1239
Citation in format AMSBIB
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\paper Quadratic stabilization of discrete-time bilinear control system
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\pages 59--79
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\pages 1222--1239
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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