標題: | Stabilization of nonlinear systems in compound critical cases |
作者: | Liaw, DC Chen, CH 電控工程研究所 Institute of Electrical and Control Engineering |
關鍵字: | nonlinear systems;stabilization;center manifold reduction |
公開日期: | 15-Aug-2002 |
摘要: | In this paper, we study the stabilization of nonlinear systems in critical cases by using the center manifold reduction technique. Three degenerate cases are considered, wherein the linearized model of the system has two zero eigenvalues, one zero eigenvalue and a pair of nonzero pure imaginary eigenvalues, or two distinct pairs of nonzero pure imaginary eigenvalues; while the remaining eigenvalues are stable. Using a local nonlinear mapping (normal form reduction) and Liapunov stability criteria, one can obtain the stability conditions for the degenerate reduced models in terms of the original system dynamics. The stabilizing control laws, in linear and/or nonlinear feedback forms, are then designed for both linearly controllable and linearly uncontrollable cases. The normal form transformations obtained in this paper have been verified by using code MACSYMA. (C) 2002 Elsevier Science Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/S0096-3003(01)00099-6 http://hdl.handle.net/11536/28585 |
ISSN: | 0096-3003 |
DOI: | 10.1016/S0096-3003(01)00099-6 |
期刊: | APPLIED MATHEMATICS AND COMPUTATION |
Volume: | 130 |
Issue: | 2-3 |
起始頁: | 317 |
結束頁: | 360 |
Appears in Collections: | Articles |
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