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Quadratic Stabilization of Discrete-Time Bilinear Systems
 
PIIS000523100000267-7-1
DOI10.31857/S000523100000267-7
Publication type Article
Status Published
Authors
Michael Khlebnikov 
Affiliation: Institute of Management Problems V.A. Trapeznikova RAS
Journal nameAvtomatika i Telemekhanika
EditionIssue 7
Pages59-79
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.

 

KeywordsDiscrete bilinear system, quadratic Lyapunov function, linear feedback, stabilizability ellipsoid, stabilizability region, linear matrix inequalities.
Received28.09.2018
Publication date29.09.2018
Number of characters621
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