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Avtomatika i Telemekhanika, 2018, Issue 7, Pages 59–79
(Mi at14959)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/at14959 https://www.mathnet.ru/eng/at/y2018/i7/p59
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Statistics & downloads: |
Abstract page: | 252 | Full-text PDF : | 29 | References: | 39 | First page: | 21 |
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