Global properties of the triangular systems in the singular case

被引：26

作者：

Korobov, V. I. ^{[2
,3
]}

Pavlichkov, S. S. ^{[1
]}

机构：

[1] Kharkov Natl Univ, Dept Math Anal, UA-61077 Kharkov, Ukraine

[2] Kharkov Natl Univ, Dept Differential Equat & Control, UA-61077 Kharkov, Ukraine

[3] Univ Szczecin, Inst Math, PL-70451 Szczecin, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 342卷 / 02期

关键词：

nonlinear robust control; triangular form; global controllability; feedback linearization;

D O I：

10.1016/j.jmaa.2007.12.070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a new class of the triangular (multi-input and multi-output) control systems, of O.D.E., which are not feedback linearizable, and investigate its global behavior. The triangular form introduced is a generalization of the classes of triangular systems, considered before. For our class, we solve the problem of global robust controllability. Combining our main result with that of [F.H. Clarke, Yu.S. Ledyaev, E.D. Sontag, A.I. Subbotin, Asymptotic controllability implies feedback stabilization, IEEE Trans. Automat. Control 42 (1997) 1394-1407], we obtain a corollary on the global discontinuous sampled stabilization (an example showing that global smooth stabilization can be irrelevant to the singular case is considered). To prove our main result, we apply a certain "back-stepping" algorithm and combine the technique proposed in [VI. Korobov, S.S. Pavlichkov, W.H. Schmidt, Global robust controllability of the triangular integro-differential Volterra systems, J. Math. Anal. Appl. 309 (2005) 743-760] with solving a specific problem of global "practical stabilization" by means of a discontinuous, time-varying feedback law. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1426 / 1439

页数：14

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