Quadratic Stabilization of Discrete-Time Bilinear 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.

Keywords

Discrete bilinear system, quadratic Lyapunov function, linear feedback, stabilizability ellipsoid, stabilizability region, linear matrix inequalities.

Received

28.09.2018

Publication date

29.09.2018

Number of characters

621

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GOST	Khlebnikov M. Quadratic Stabilization of Discrete-Time Bilinear Systems // Avtomatika i Telemekhanika – 2018. – Issue 7 C. 59-79 [Electronic resource]. URL: http://ras.jes.su/ait/s000523100000267-7-1-en (circulation date: 25.03.2025). DOI: 10.31857/S000523100000267-7
MLA	Khlebnikov, Michael "Quadratic Stabilization of Discrete-Time Bilinear Systems." Avtomatika i Telemekhanika 7 (2018):59-79. DOI: 10.31857/S000523100000267-7
APA	Khlebnikov M. (2018). Quadratic Stabilization of Discrete-Time Bilinear Systems. Avtomatika i Telemekhanika (7), pp.59-79 DOI: 10.31857/S000523100000267-7

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