chapter  10
10 Pages

Estimation of Attractors and Invariant Domains for Perturbed Complex and Large-Scale Systems

WithP. Borne, G. Dauphin-Tanguy, J.-P. Richard

This chapter concerns the stability study of perturbed nonlinear and complex systems. The approach is based on the definition of specific comparison systems (Grujić et al., 1987; Matrosov, 1968; Wazewski, 1950) deduced from the initial model of the process by means of an overvaluation (Borne and Gentina, 1974; Gentina et al., 1972; Grujić et al., 1976; Richard et al., 1988) valid on a given domain ℱ. Such an approach enables the estimation of attractors and regions of attraction (Bhatia and Szegö, 1970) for locally stable or unstable systems (Borne et al., 1990) influenced by unknown perturbations with possible stochastic origin.