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Stabilizability of second-order Quadratic Differential Equations:

Automatic Control, IEEE Transactions on

D.E. Koditschek* and K.S. Narendra†
*University of Pennsylvania †Yale University

Full PDF | Penn Scholarly Commons

Abstract
This paper investigates the stability properties of second-order systems.dot{x} = f(x), wheref(x)contains either quadratic terms-system (1)-or linear and quadratic terms-system (2)-inx. The principal contributions are summarized in two theorems which give necessary, and sufficient conditions for stability and asymptotic stability in the large of systems (1) and (2), respectively.
BibTeX entry
@ARTICLE{1103016, 
author={ Koditschek, D. and Narendra, K.}, 
journal={Automatic Control, IEEE Transactions on}, 
title={The stability of second-order quadratic differential equations}, 
year={1982}, 
month={aug}, 
volume={27}, 
number={4}, 
pages={ 783 - 798}, 
keywords={ Asymptotic stability, nonlinear systems; Nonlinear differential equations; Stability, nonlinear systems;}, 
doi={10.1109/TAC.1982.1103016}, 
ISSN={0018-9286},}
}

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