Perturbations of nonlinear systems of neutral type
Nonlinear, time-dependent dynamical systems of neutral type are considered. Under suitable hypotheses on systems parameters some differentiability results concerning the solution are proved. Genericity of some properties of solution is also studied. Next, the nonlinear variation of parameters formula for neutral systems with nonlinear perturbation is derived. This formula is proved for large class of initial functions. The asymptotic behavior of neutral systems with nonlinear perturbations mentioned in the paper is of great importance when dealing with control systems with limited power. The paper contains many remarks, corollaries and comments concerning solution of neutral systems. Similar problems have been treated by \textit{G. A. Shanholt} [Math. Systems Theory 6 (1972), 343-352 (1973; Zbl 0248.34070)] and by \textit{G. Tadmor} [J. Differ. Equations 51, 151-181 (1984; Zbl 0547.34058)].
Nonlinear, time-dependent dynamical systems of neutral type
nonlinear variation of parameters formula
neutral systems with nonlinear perturbation
scientific article; zbMATH DE number 4127666