On the asymptotical behaviour of solutions of a class of nonlinear control systems (Q1579186)

The author is interested in the asymptotic behavior of solutions to a nonlinear system of the form \[ \dot x= Ax+ B\phi(\sigma),\quad \sigma= C^Tx, \] where \(\phi\) is a continuous function satisfying certain sector conditions. The system is said to be dichotomous if any bounded solution is attracted by the set of equilibrium points \(D\), and globally asymptotic if every solution is attracted by \(D\). On the basis of a LaSalle's invariance principle of integral type, the author gives some sufficient conditions for dichotomy and for global asymptotic behavior.