Quadratic Stabilization of Discrete-Time Bilinear Systems

被引：0
作者：
M. V. Khlebnikov
机构：
[1] Russian Academy of Sciences,Trapeznikov Institute of Control Sciences
来源：
Automation and Remote Control | 2018年 / 79卷
关键词：
discrete-time bilinear system; quadratic Lyapunov function; linear feedback; stabilizability ellipsoid; domain of stabilizability; linear matrix inequalities;
D O I：
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学科分类号：
摘要：
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.
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页码：1222 / 1239
页数：17
相关论文
共 41 条
[1]  
Emel’yanov S.V.(2012)Stabilizability of Bilinear Systems of Canonical Form Dokl. Math. 86 591-594
[2]  
Krishchenko A.P.(2000)Stabilization of Bilinear Systems on the Plane by Constant and Relay Controls Differ. Equat. 36 1131-1138
[3]  
Emel’yanov S.V.(1983)On Asymptotically Stabilizing Feedback Control of Bilinear Systems IEEE Trans. Autom. Control 28 863-864
[4]  
Korovin S.K.(1991)Stability Analysis of Bilinear Systems IEEE Trans. Autom. Control 36 1310-1315
[5]  
Shepit’ko A.S.(2000)The Method of Rotating Lyapunov Functions in the Stabilization Problem for Two-dimensional Bilinear Systems Differ. Equat. 36 1262-1265
[6]  
Ryan E.(2002)Stabilization of Two-Dimensional Single-Input Bilinear Systems with a Finite Number of Constant Feedback Controllers Proc. Am. Control Conf. 3 1874-1879
[7]  
Buckingham N.(1990)On the Global Linearization of Bilinear Systems Syst. Control Lett. 15 433-439
[8]  
Chen L.K.(1993)On the Stabilization of the Homogeneous Bilinear Systems Syst. Control Lett. 21 503-510
[9]  
Yang X.(2004)Asymptotic Observers for Some Classes of Bilinear Systems with Linear Input Dokl. Math., Control Theory 398 38-43
[10]  
Mohler R.R.(2002)Design of Linear Feedback for Bilinear Control Systems Int. J. Appl. Math. Comput. Sci. 11 493-511
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