IEEE Transactions on Automatic Control, vol. 54, pp. 1042-1047, 2009 (with A. Packard).
@ARTICLE{4908958,
title={Local Stability Analysis for Uncertain Nonlinear Systems},
author={Topcu, U. and Packard, A.},
journal={Automatic Control, IEEE Transactions on},
year={2009},
month={May },
volume={54},
number={5},
pages={1042-1047},
abstract={We propose a method to compute provably invariant subsets of the region-of-attraction for the asymptotically stable equilibrium points of uncertain nonlinear dynamical systems. We consider polynomial dynamics with perturbations that either obey local polynomial bounds or are described by uncertain parameters multiplying polynomial terms in the vector field. This uncertainty description is motivated by both incapabilities in modeling, as well as bilinearity and dimension of the sum-of-squares programming problems whose solutions provide invariant subsets of the region-of-attraction. We demonstrate the method on three examples from the literature and a controlled short period aircraft dynamics example.},
keywords={asymptotic stability, nonlinear control systems, polynomials, uncertain systemsasymptotic stability, local stability analysis, polynomial dynamics, sum-of-squares programming problems, uncertain nonlinear dynamical systems},
doi={10.1109/TAC.2009.2017157},
ISSN={0018-9286},
}